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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 97020cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.cu4 | 97020cv1 | \([0, 0, 0, -19992, 1065701]\) | \(643956736/15125\) | \(20755401282000\) | \([2]\) | \(248832\) | \(1.3408\) | \(\Gamma_0(N)\)-optimal |
| 97020.cu3 | 97020cv2 | \([0, 0, 0, -44247, -2024386]\) | \(436334416/171875\) | \(3773709324000000\) | \([2]\) | \(497664\) | \(1.6874\) | |
| 97020.cu2 | 97020cv3 | \([0, 0, 0, -196392, -33076519]\) | \(610462990336/8857805\) | \(12155193206790480\) | \([2]\) | \(746496\) | \(1.8901\) | |
| 97020.cu1 | 97020cv4 | \([0, 0, 0, -3131247, -2132671786]\) | \(154639330142416/33275\) | \(730590125126400\) | \([2]\) | \(1492992\) | \(2.2367\) |
Rank
sage: E.rank()
The elliptic curves in class 97020cv have rank \(0\).
Complex multiplication
The elliptic curves in class 97020cv do not have complex multiplication.Modular form 97020.2.a.cv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
