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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 96330db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96330.dc4 | 96330db1 | \([1, 0, 0, 2109, -32319]\) | \(214921799/218880\) | \(-1056491953920\) | \([2]\) | \(245760\) | \(0.99401\) | \(\Gamma_0(N)\)-optimal |
| 96330.dc3 | 96330db2 | \([1, 0, 0, -11411, -300015]\) | \(34043726521/11696400\) | \(56456288787600\) | \([2, 2]\) | \(491520\) | \(1.3406\) | |
| 96330.dc2 | 96330db3 | \([1, 0, 0, -75631, 7778861]\) | \(9912050027641/311647500\) | \(1504262957827500\) | \([2]\) | \(983040\) | \(1.6872\) | |
| 96330.dc1 | 96330db4 | \([1, 0, 0, -163511, -25457355]\) | \(100162392144121/23457780\) | \(113226223624020\) | \([2]\) | \(983040\) | \(1.6872\) |
Rank
sage: E.rank()
The elliptic curves in class 96330db have rank \(0\).
Complex multiplication
The elliptic curves in class 96330db do not have complex multiplication.Modular form 96330.2.a.db
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
