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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1872.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.g1 | 1872k2 | \([0, 0, 0, -1011, -12366]\) | \(1033364331/676\) | \(74760192\) | \([2]\) | \(768\) | \(0.45049\) | |
| 1872.g2 | 1872k1 | \([0, 0, 0, -51, -270]\) | \(-132651/208\) | \(-23003136\) | \([2]\) | \(384\) | \(0.10392\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.g do not have complex multiplication.Modular form 1872.2.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.
