Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 139230.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139230.g1 | 139230eq2 | \([1, -1, 0, -6630, -195364]\) | \(1637607620403/95728360\) | \(1884221309880\) | \([2]\) | \(313344\) | \(1.1089\) | |
139230.g2 | 139230eq1 | \([1, -1, 0, -1230, 13076]\) | \(10460353203/2475200\) | \(48719361600\) | \([2]\) | \(156672\) | \(0.76232\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139230.g have rank \(0\).
Complex multiplication
The elliptic curves in class 139230.g do not have complex multiplication.Modular form 139230.2.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.