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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 75348.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75348.g1 | 75348c2 | \([0, 0, 0, -3015, -5346]\) | \(16241202000/9332687\) | \(1741703378688\) | \([2]\) | \(92160\) | \(1.0385\) | |
| 75348.g2 | 75348c1 | \([0, 0, 0, -1980, 33777]\) | \(73598976000/336973\) | \(3930453072\) | \([2]\) | \(46080\) | \(0.69188\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75348.g have rank \(2\).
Complex multiplication
The elliptic curves in class 75348.g do not have complex multiplication.Modular form 75348.2.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.
