Properties

Label 637.c
Number of curves 22
Conductor 637637
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 637.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
637.c1 637a1 [1,1,0,107,454][1, -1, 0, -107, 454] 56723625/13-56723625/13 31213-31213 [][] 6060 0.14604-0.14604 Γ0(N)\Gamma_0(N)-optimal
637.c2 637a2 [1,1,0,628,17823][1, -1, 0, 628, -17823] 11397810375/6274851711397810375/62748517 150659189317-150659189317 [][] 420420 0.826910.82691  

Rank

sage: E.rank()
 

The elliptic curves in class 637.c have rank 11.

Complex multiplication

The elliptic curves in class 637.c do not have complex multiplication.

Modular form 637.2.a.c

sage: E.q_eigenform(10)
 
q+q2q43q83q93q11q13q16+7q173q187q19+O(q20)q + q^{2} - q^{4} - 3 q^{8} - 3 q^{9} - 3 q^{11} - q^{13} - q^{16} + 7 q^{17} - 3 q^{18} - 7 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.

(1771)\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.