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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 402930d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402930.d2 | 402930d1 | \([1, -1, 0, 2886735, -1560914019]\) | \(55619170283328813/54171700000000\) | \(-2591148717639900000000\) | \([2]\) | \(28508160\) | \(2.7959\) | \(\Gamma_0(N)\)-optimal* |
402930.d1 | 402930d2 | \([1, -1, 0, -15263265, -14204204019]\) | \(8221407719957471187/2934573080890000\) | \(140366930987373370830000\) | \([2]\) | \(57016320\) | \(3.1425\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 402930d have rank \(0\).
Complex multiplication
The elliptic curves in class 402930d do not have complex multiplication.Modular form 402930.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.