Properties

Label 3024.z
Number of curves 22
Conductor 30243024
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 3024.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3024.z1 3024p2 [0,0,0,111,502][0, 0, 0, -111, -502] 2431344/343-2431344/343 21337344-21337344 [][] 864864 0.137500.13750  
3024.z2 3024p1 [0,0,0,9,2][0, 0, 0, 9, 2] 11664/711664/7 48384-48384 [][] 288288 0.41181-0.41181 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3024.z have rank 00.

Complex multiplication

The elliptic curves in class 3024.z do not have complex multiplication.

Modular form 3024.2.a.z

sage: E.q_eigenform(10)
 
q+3q5q73q11+2q136q175q19+O(q20)q + 3 q^{5} - q^{7} - 3 q^{11} + 2 q^{13} - 6 q^{17} - 5 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 LMFDB numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.