Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 810.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
810.g1 | 810f2 | \([1, -1, 1, -218, -1943]\) | \(-2146689/2000\) | \(-1062882000\) | \([]\) | \(432\) | \(0.42854\) | |
810.g2 | 810f1 | \([1, -1, 1, 22, 41]\) | \(15166431/20480\) | \(-1658880\) | \([3]\) | \(144\) | \(-0.12077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 810.g have rank \(0\).
Complex multiplication
The elliptic curves in class 810.g do not have complex multiplication.Modular form 810.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.