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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 242760s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.s4 | 242760s1 | \([0, -1, 0, -75236, 12242436]\) | \(-7622072656/6024375\) | \(-37225924414560000\) | \([2]\) | \(1769472\) | \(1.8782\) | \(\Gamma_0(N)\)-optimal |
| 242760.s3 | 242760s2 | \([0, -1, 0, -1375736, 621396636]\) | \(11650266200164/3186225\) | \(78753511205913600\) | \([2, 2]\) | \(3538944\) | \(2.2247\) | |
| 242760.s1 | 242760s3 | \([0, -1, 0, -22010336, 39752852076]\) | \(23855046548417282/1785\) | \(88239228241920\) | \([2]\) | \(7077888\) | \(2.5713\) | |
| 242760.s2 | 242760s4 | \([0, -1, 0, -1549136, 455001996]\) | \(8317046918882/3008008815\) | \(148697129624925665280\) | \([2]\) | \(7077888\) | \(2.5713\) |
Rank
sage: E.rank()
The elliptic curves in class 242760s have rank \(1\).
Complex multiplication
The elliptic curves in class 242760s do not have complex multiplication.Modular form 242760.2.a.s
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.
