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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 97020w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.cr1 | 97020w1 | \([0, 0, 0, -296352, 40387221]\) | \(226492416/75625\) | \(961078856363010000\) | \([2]\) | \(1290240\) | \(2.1532\) | \(\Gamma_0(N)\)-optimal |
| 97020.cr2 | 97020w2 | \([0, 0, 0, 861273, 278626446]\) | \(347482224/366025\) | \(-74425946636751494400\) | \([2]\) | \(2580480\) | \(2.4997\) |
Rank
sage: E.rank()
The elliptic curves in class 97020w have rank \(1\).
Complex multiplication
The elliptic curves in class 97020w do not have complex multiplication.Modular form 97020.2.a.w
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.
