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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2600.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2600.g1 | 2600d2 | \([0, 0, 0, -5875, 168750]\) | \(5606442/169\) | \(676000000000\) | \([2]\) | \(3200\) | \(1.0464\) | |
| 2600.g2 | 2600d1 | \([0, 0, 0, -875, -6250]\) | \(37044/13\) | \(26000000000\) | \([2]\) | \(1600\) | \(0.69980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2600.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2600.g do not have complex multiplication.Modular form 2600.2.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.
