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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 491970d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
491970.d2 | 491970d1 | \([1, 1, 0, 1183627, -2193261267]\) | \(1238798620042199/14760960000000\) | \(-2185151836093440000000\) | \([2]\) | \(34062336\) | \(2.7756\) | \(\Gamma_0(N)\)-optimal* |
491970.d1 | 491970d2 | \([1, 1, 0, -19807093, -31660034003]\) | \(5805223604235668521/435937500000000\) | \(64534395360937500000000\) | \([2]\) | \(68124672\) | \(3.1221\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 491970d have rank \(1\).
Complex multiplication
The elliptic curves in class 491970d do not have complex multiplication.Modular form 491970.2.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.