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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 242760.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.k1 | 242760k2 | \([0, -1, 0, -71392616, -193161993684]\) | \(3999510942669935909746/712181767349390625\) | \(7165847599078514976000000\) | \([2]\) | \(60383232\) | \(3.4886\) | |
| 242760.k2 | 242760k1 | \([0, -1, 0, 8608704, -17383093380]\) | \(14024593011218005948/34054756997160375\) | \(-171326485634098096512000\) | \([2]\) | \(30191616\) | \(3.1421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242760.k have rank \(1\).
Complex multiplication
The elliptic curves in class 242760.k do not have complex multiplication.Modular form 242760.2.a.k
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
