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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 468270.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.l1 | 468270l2 | \([1, -1, 0, -21196500210, 1187808122415316]\) | \(815516123997553004685843001/168699801600\) | \(217870390143054950400\) | \([2]\) | \(389283840\) | \(4.1998\) | \(\Gamma_0(N)\)-optimal* |
468270.l2 | 468270l1 | \([1, -1, 0, -1324776690, 18559884843220]\) | \(-199098554419711270541881/2863609298288640\) | \(-3698259684470345076572160\) | \([2]\) | \(194641920\) | \(3.8532\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270.l have rank \(1\).
Complex multiplication
The elliptic curves in class 468270.l do not have complex multiplication.Modular form 468270.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.