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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 112659.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112659.g1 | 112659h2 | \([0, 1, 1, -131067, 18230120]\) | \(-23100424192/14739\) | \(-158874854734131\) | \([]\) | \(625968\) | \(1.6658\) | |
112659.g2 | 112659h1 | \([0, 1, 1, 1473, 105275]\) | \(32768/459\) | \(-4947659836011\) | \([]\) | \(208656\) | \(1.1165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 112659.g have rank \(1\).
Complex multiplication
The elliptic curves in class 112659.g do not have complex multiplication.Modular form 112659.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.