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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2420.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2420.g1 | 2420f2 | \([0, -1, 0, -7300, -237048]\) | \(94875856/275\) | \(124717894400\) | \([2]\) | \(2880\) | \(0.99987\) | |
2420.g2 | 2420f1 | \([0, -1, 0, -645, -130]\) | \(1048576/605\) | \(17148710480\) | \([2]\) | \(1440\) | \(0.65330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2420.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2420.g do not have complex multiplication.Modular form 2420.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.