Properties

Label 343824ca
Number of curves 44
Conductor 343824343824
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 343824ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
343824.ca4 343824ca1 [0,1,0,1004596632,12216145084308][0, 1, 0, -1004596632, 12216145084308] 27374041292637614212993237273/10105156631438781237748827374041292637614212993237273/101051566314387812377488 413907215623732479498190848413907215623732479498190848 [2][2] 245514240245514240 3.96753.9675 Γ0(N)\Gamma_0(N)-optimal
343824.ca2 343824ca2 [0,1,0,16059278552,783310931153940][0, 1, 0, -16059278552, 783310931153940] 111825759760338976846738658338393/1532291201797601099556111825759760338976846738658338393/1532291201797601099556 62762647625629741037813766276264762562974103781376 [2,2][2, 2] 491028480491028480 4.31404.3140  
343824.ca1 343824ca3 [0,1,0,256948455992,50132156888525268][0, 1, 0, -256948455992, 50132156888525268] 458038307459437803276572539343003833/86000447460798458038307459437803276572539343003833/86000447460798 352257832799428608352257832799428608 [2][2] 982056960982056960 4.66064.6606  
343824.ca3 343824ca4 [0,1,0,16045011832,784772157149780][0, 1, 0, -16045011832, 784772157149780] 111527993597885114164012178708473/413980765601504764798430334-111527993597885114164012178708473/413980765601504764798430334 1695665215903763516614370648064-1695665215903763516614370648064 [2][2] 982056960982056960 4.66064.6606  

Rank

sage: E.rank()
 

The elliptic curves in class 343824ca have rank 00.

Complex multiplication

The elliptic curves in class 343824ca do not have complex multiplication.

Modular form 343824.2.a.ca

sage: E.q_eigenform(10)
 
q+q3+2q54q7+q9+4q11+q13+2q15+2q17+q19+O(q20)q + q^{3} + 2 q^{5} - 4 q^{7} + q^{9} + 4 q^{11} + q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.