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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7920a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7920.a1 | 7920a1 | \([0, 0, 0, -2403, -45198]\) | \(76136652/275\) | \(5542732800\) | \([2]\) | \(7680\) | \(0.73076\) | \(\Gamma_0(N)\)-optimal |
7920.a2 | 7920a2 | \([0, 0, 0, -1323, -86022]\) | \(-6353046/75625\) | \(-3048503040000\) | \([2]\) | \(15360\) | \(1.0773\) |
Rank
sage: E.rank()
The elliptic curves in class 7920a have rank \(1\).
Complex multiplication
The elliptic curves in class 7920a do not have complex multiplication.Modular form 7920.2.a.a
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.