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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 15246c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.q1 | 15246c1 | \([1, -1, 0, -25977, 1618029]\) | \(-4904170882875/43904\) | \(-17355558528\) | \([3]\) | \(28224\) | \(1.1304\) | \(\Gamma_0(N)\)-optimal |
15246.q2 | 15246c2 | \([1, -1, 0, -13272, 3187520]\) | \(-897199875/14680064\) | \(-4230483271483392\) | \([]\) | \(84672\) | \(1.6797\) |
Rank
sage: E.rank()
The elliptic curves in class 15246c have rank \(1\).
Complex multiplication
The elliptic curves in class 15246c do not have complex multiplication.Modular form 15246.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.