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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 116242g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.l2 | 116242g1 | \([1, 1, 0, -5061, -37555]\) | \(304821217/164864\) | \(7756172125184\) | \([2]\) | \(288000\) | \(1.1643\) | \(\Gamma_0(N)\)-optimal |
116242.l1 | 116242g2 | \([1, 1, 0, -62821, -6079251]\) | \(582810602977/829472\) | \(39023241004832\) | \([2]\) | \(576000\) | \(1.5109\) |
Rank
sage: E.rank()
The elliptic curves in class 116242g have rank \(1\).
Complex multiplication
The elliptic curves in class 116242g do not have complex multiplication.Modular form 116242.2.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.