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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 296240bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296240.bs4 | 296240bs1 | \([0, 0, 0, 11638, 1131531]\) | \(73598976/276115\) | \(-653998871859760\) | \([2]\) | \(675840\) | \(1.5257\) | \(\Gamma_0(N)\)-optimal |
| 296240.bs3 | 296240bs2 | \([0, 0, 0, -117967, 13651374]\) | \(4790692944/648025\) | \(24558324984121600\) | \([2, 2]\) | \(1351680\) | \(1.8722\) | |
| 296240.bs1 | 296240bs3 | \([0, 0, 0, -1821347, 946081586]\) | \(4407931365156/100625\) | \(15253618002560000\) | \([4]\) | \(2703360\) | \(2.2188\) | |
| 296240.bs2 | 296240bs4 | \([0, 0, 0, -488267, -117508886]\) | \(84923690436/9794435\) | \(1484726161897180160\) | \([2]\) | \(2703360\) | \(2.2188\) |
Rank
sage: E.rank()
The elliptic curves in class 296240bs have rank \(1\).
Complex multiplication
The elliptic curves in class 296240bs do not have complex multiplication.Modular form 296240.2.a.bs
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.
