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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 25200.el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.el1 | 25200bm4 | \([0, 0, 0, -147675, 21798250]\) | \(15267472418/36015\) | \(840157920000000\) | \([4]\) | \(98304\) | \(1.7437\) | |
| 25200.el2 | 25200bm2 | \([0, 0, 0, -12675, 63250]\) | \(19307236/11025\) | \(128595600000000\) | \([2, 2]\) | \(49152\) | \(1.3971\) | |
| 25200.el3 | 25200bm1 | \([0, 0, 0, -8175, -283250]\) | \(20720464/105\) | \(306180000000\) | \([2]\) | \(24576\) | \(1.0505\) | \(\Gamma_0(N)\)-optimal |
| 25200.el4 | 25200bm3 | \([0, 0, 0, 50325, 504250]\) | \(604223422/354375\) | \(-8266860000000000\) | \([2]\) | \(98304\) | \(1.7437\) |
Rank
sage: E.rank()
The elliptic curves in class 25200.el have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.el do not have complex multiplication.Modular form 25200.2.a.el
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.
