Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 75150.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75150.g1 | 75150c2 | \([1, -1, 0, -126942, 16977716]\) | \(735580702683/22311200\) | \(6861739837500000\) | \([2]\) | \(460800\) | \(1.8149\) | |
| 75150.g2 | 75150c1 | \([1, -1, 0, -18942, -626284]\) | \(2444008923/855040\) | \(262964880000000\) | \([2]\) | \(230400\) | \(1.4683\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75150.g have rank \(1\).
Complex multiplication
The elliptic curves in class 75150.g do not have complex multiplication.Modular form 75150.2.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.
