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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3025.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3025.f1 | 3025b3 | \([1, -1, 0, -179042, -29107259]\) | \(22930509321/6875\) | \(190304404296875\) | \([2]\) | \(11520\) | \(1.7180\) | |
| 3025.f2 | 3025b4 | \([1, -1, 0, -88292, 9884991]\) | \(2749884201/73205\) | \(2026361296953125\) | \([2]\) | \(11520\) | \(1.7180\) | |
| 3025.f3 | 3025b2 | \([1, -1, 0, -12667, -324384]\) | \(8120601/3025\) | \(83733937890625\) | \([2, 2]\) | \(5760\) | \(1.3714\) | |
| 3025.f4 | 3025b1 | \([1, -1, 0, 2458, -37009]\) | \(59319/55\) | \(-1522435234375\) | \([2]\) | \(2880\) | \(1.0249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3025.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3025.f do not have complex multiplication.Modular form 3025.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
