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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 7800.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7800.e1 | 7800o3 | \([0, -1, 0, -247408, -22467188]\) | \(52337949619538/23423590125\) | \(749554884000000000\) | \([2]\) | \(73728\) | \(2.1253\) | |
| 7800.e2 | 7800o2 | \([0, -1, 0, -122408, 16282812]\) | \(12677589459076/213890625\) | \(3422250000000000\) | \([2, 2]\) | \(36864\) | \(1.7787\) | |
| 7800.e3 | 7800o1 | \([0, -1, 0, -121908, 16423812]\) | \(50091484483024/14625\) | \(58500000000\) | \([4]\) | \(18432\) | \(1.4321\) | \(\Gamma_0(N)\)-optimal |
| 7800.e4 | 7800o4 | \([0, -1, 0, -5408, 46000812]\) | \(-546718898/28564453125\) | \(-914062500000000000\) | \([2]\) | \(73728\) | \(2.1253\) |
Rank
sage: E.rank()
The elliptic curves in class 7800.e have rank \(1\).
Complex multiplication
The elliptic curves in class 7800.e do not have complex multiplication.Modular form 7800.2.a.e
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.
