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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 424830.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.g1 | 424830g2 | \([1, 1, 0, -768023, 258745677]\) | \(-12242088317612041/600\) | \(-2455517400\) | \([]\) | \(2939328\) | \(1.7255\) | \(\Gamma_0(N)\)-optimal* |
424830.g2 | 424830g1 | \([1, 1, 0, -9398, 358002]\) | \(-22434194041/843750\) | \(-3453071343750\) | \([]\) | \(979776\) | \(1.1762\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.g have rank \(1\).
Complex multiplication
The elliptic curves in class 424830.g do not have complex multiplication.Modular form 424830.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.