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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 4025.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4025.g1 | 4025b1 | \([1, -1, 0, -4067, -98784]\) | \(476196576129/197225\) | \(3081640625\) | \([2]\) | \(3456\) | \(0.78270\) | \(\Gamma_0(N)\)-optimal |
| 4025.g2 | 4025b2 | \([1, -1, 0, -3442, -130659]\) | \(-288673724529/311181605\) | \(-4862212578125\) | \([2]\) | \(6912\) | \(1.1293\) |
Rank
sage: E.rank()
The elliptic curves in class 4025.g have rank \(0\).
Complex multiplication
The elliptic curves in class 4025.g do not have complex multiplication.Modular form 4025.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
