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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 423024l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
423024.l2 | 423024l1 | \([0, -1, 0, -18040576, -29589168128]\) | \(-158531287603583609503489/634774607963040384\) | \(-2600036794216613412864\) | \([]\) | \(22861440\) | \(2.9660\) | \(\Gamma_0(N)\)-optimal* |
423024.l1 | 423024l2 | \([0, -1, 0, -18715936, 2447652399232]\) | \(-177010260681338006596129/631757862884385194481594\) | \(-2587680206374441756596609024\) | \([]\) | \(160030080\) | \(3.9390\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 423024l have rank \(1\).
Complex multiplication
The elliptic curves in class 423024l do not have complex multiplication.Modular form 423024.2.a.l
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.