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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 59248y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59248.p3 | 59248y1 | \([0, 0, 0, -31211, -2068390]\) | \(5545233/161\) | \(97623155216384\) | \([2]\) | \(168960\) | \(1.4621\) | \(\Gamma_0(N)\)-optimal |
| 59248.p2 | 59248y2 | \([0, 0, 0, -73531, 4745130]\) | \(72511713/25921\) | \(15717327989837824\) | \([2, 2]\) | \(337920\) | \(1.8087\) | |
| 59248.p4 | 59248y3 | \([0, 0, 0, 222709, 33361914]\) | \(2014698447/1958887\) | \(-1187780929517744128\) | \([2]\) | \(675840\) | \(2.1553\) | |
| 59248.p1 | 59248y4 | \([0, 0, 0, -1046891, 412193626]\) | \(209267191953/55223\) | \(33484742239219712\) | \([4]\) | \(675840\) | \(2.1553\) |
Rank
sage: E.rank()
The elliptic curves in class 59248y have rank \(0\).
Complex multiplication
The elliptic curves in class 59248y do not have complex multiplication.Modular form 59248.2.a.y
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.
