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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 97020cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.cb2 | 97020cd1 | \([0, 0, 0, -214032, 31702804]\) | \(1007878144/179685\) | \(193314147108445440\) | \([]\) | \(870912\) | \(2.0362\) | \(\Gamma_0(N)\)-optimal |
| 97020.cb1 | 97020cd2 | \([0, 0, 0, -16513392, 25828699876]\) | \(462893166690304/4125\) | \(4437882165024000\) | \([3]\) | \(2612736\) | \(2.5855\) |
Rank
sage: E.rank()
The elliptic curves in class 97020cd have rank \(0\).
Complex multiplication
The elliptic curves in class 97020cd do not have complex multiplication.Modular form 97020.2.a.cd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
