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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 214774.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214774.d1 | 214774m2 | \([1, -1, 0, -6602387, -6528145163]\) | \(2616032722429824267375/129231424\) | \(1572358735808\) | \([2]\) | \(2875392\) | \(2.2635\) | |
214774.d2 | 214774m1 | \([1, -1, 0, -412627, -101936331]\) | \(-638577663082635375/141954125824\) | \(-1727155848900608\) | \([2]\) | \(1437696\) | \(1.9169\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214774.d have rank \(0\).
Complex multiplication
The elliptic curves in class 214774.d do not have complex multiplication.Modular form 214774.2.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 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.