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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 363726d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.d2 | 363726d1 | \([1, -1, 0, -130708881, 575215303581]\) | \(191229709259204053417/3174336\) | \(4099553266843584\) | \([]\) | \(43130880\) | \(2.9924\) | \(\Gamma_0(N)\)-optimal |
363726.d1 | 363726d2 | \([1, -1, 0, -131509296, 567814323456]\) | \(194764335462520004377/4875157440823296\) | \(6296109678655299773005824\) | \([]\) | \(129392640\) | \(3.5417\) |
Rank
sage: E.rank()
The elliptic curves in class 363726d have rank \(1\).
Complex multiplication
The elliptic curves in class 363726d do not have complex multiplication.Modular form 363726.2.a.d
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.