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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 493680g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.g2 | 493680g1 | \([0, -1, 0, -908832976, -10537393816640]\) | \(8595711443128766579/7520256000000\) | \(72631788629724758016000000\) | \([2]\) | \(273715200\) | \(3.8880\) | \(\Gamma_0(N)\)-optimal |
493680.g1 | 493680g2 | \([0, -1, 0, -14538272976, -674705456792640]\) | \(35185850652034529726579/26967168000\) | \(260453054539403624448000\) | \([2]\) | \(547430400\) | \(4.2346\) |
Rank
sage: E.rank()
The elliptic curves in class 493680g have rank \(1\).
Complex multiplication
The elliptic curves in class 493680g do not have complex multiplication.Modular form 493680.2.a.g
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.