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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 33600.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.ej1 | 33600ce4 | \([0, 1, 0, -180033, -29459937]\) | \(157551496201/13125\) | \(53760000000000\) | \([2]\) | \(196608\) | \(1.6785\) | |
| 33600.ej2 | 33600ce2 | \([0, 1, 0, -12033, -395937]\) | \(47045881/11025\) | \(45158400000000\) | \([2, 2]\) | \(98304\) | \(1.3319\) | |
| 33600.ej3 | 33600ce1 | \([0, 1, 0, -4033, 92063]\) | \(1771561/105\) | \(430080000000\) | \([2]\) | \(49152\) | \(0.98533\) | \(\Gamma_0(N)\)-optimal |
| 33600.ej4 | 33600ce3 | \([0, 1, 0, 27967, -2435937]\) | \(590589719/972405\) | \(-3982970880000000\) | \([2]\) | \(196608\) | \(1.6785\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.ej do not have complex multiplication.Modular form 33600.2.a.ej
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.
