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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 265200.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 265200.j1 | 265200j3 | \([0, -1, 0, -559408, 155509312]\) | \(302503589987689/12214946250\) | \(781756560000000000\) | \([2]\) | \(4718592\) | \(2.1994\) | |
| 265200.j2 | 265200j2 | \([0, -1, 0, -91408, -7354688]\) | \(1319778683209/395612100\) | \(25319174400000000\) | \([2, 2]\) | \(2359296\) | \(1.8529\) | |
| 265200.j3 | 265200j1 | \([0, -1, 0, -83408, -9242688]\) | \(1002702430729/159120\) | \(10183680000000\) | \([2]\) | \(1179648\) | \(1.5063\) | \(\Gamma_0(N)\)-optimal |
| 265200.j4 | 265200j4 | \([0, -1, 0, 248592, -49514688]\) | \(26546265663191/31856082570\) | \(-2038789284480000000\) | \([2]\) | \(4718592\) | \(2.1994\) |
Rank
sage: E.rank()
The elliptic curves in class 265200.j have rank \(1\).
Complex multiplication
The elliptic curves in class 265200.j do not have complex multiplication.Modular form 265200.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
