Properties

Label 612.d
Number of curves 22
Conductor 612612
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 612.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
612.d1 612a1 [0,0,0,456,3748][0, 0, 0, -456, 3748] 1517101056/17-1517101056/17 117504-117504 [3][3] 144144 0.125850.12585 Γ0(N)\Gamma_0(N)-optimal
612.d2 612a2 [0,0,0,216,7668][0, 0, 0, -216, 7668] 221184/4913-221184/4913 24755860224-24755860224 [][] 432432 0.675150.67515  

Rank

sage: E.rank()
 

The elliptic curves in class 612.d have rank 00.

Complex multiplication

The elliptic curves in class 612.d do not have complex multiplication.

Modular form 612.2.a.d

sage: E.q_eigenform(10)
 
q+3q5+2q7+3q11q13q177q19+O(q20)q + 3 q^{5} + 2 q^{7} + 3 q^{11} - q^{13} - q^{17} - 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.

(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.