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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2475.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2475.e1 | 2475k1 | \([0, 0, 1, -5250, -153594]\) | \(-56197120/3267\) | \(-930329296875\) | \([]\) | \(2880\) | \(1.0528\) | \(\Gamma_0(N)\)-optimal |
| 2475.e2 | 2475k2 | \([0, 0, 1, 28500, -271719]\) | \(8990228480/5314683\) | \(-1513439026171875\) | \([3]\) | \(8640\) | \(1.6021\) |
Rank
sage: E.rank()
The elliptic curves in class 2475.e have rank \(0\).
Complex multiplication
The elliptic curves in class 2475.e do not have complex multiplication.Modular form 2475.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
