Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 141610.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.g1 | 141610bo1 | \([1, 0, 1, -106503, -11596294]\) | \(47045881/6800\) | \(19310373815910800\) | \([2]\) | \(1658880\) | \(1.8503\) | \(\Gamma_0(N)\)-optimal |
141610.g2 | 141610bo2 | \([1, 0, 1, 176717, -62689182]\) | \(214921799/722500\) | \(-2051727217940522500\) | \([2]\) | \(3317760\) | \(2.1968\) |
Rank
sage: E.rank()
The elliptic curves in class 141610.g have rank \(1\).
Complex multiplication
The elliptic curves in class 141610.g do not have complex multiplication.Modular form 141610.2.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.