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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 463680.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.p1 | 463680p2 | \([0, 0, 0, -971988, 368838752]\) | \(918296036195902272/7157176915\) | \(791526509383680\) | \([2]\) | \(4423680\) | \(2.0322\) | \(\Gamma_0(N)\)-optimal* |
463680.p2 | 463680p1 | \([0, 0, 0, -59463, 6018812]\) | \(-13456137700214208/1269407748175\) | \(-2193536588846400\) | \([2]\) | \(2211840\) | \(1.6856\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 463680.p have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.p do not have complex multiplication.Modular form 463680.2.a.p
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.