Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 142912bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142912.t2 | 142912bn1 | \([0, -1, 0, -393, 3025]\) | \(6572128000/270193\) | \(276677632\) | \([]\) | \(41472\) | \(0.38532\) | \(\Gamma_0(N)\)-optimal |
142912.t1 | 142912bn2 | \([0, -1, 0, -4793, -125279]\) | \(11894238688000/92019697\) | \(94228169728\) | \([]\) | \(124416\) | \(0.93463\) |
Rank
sage: E.rank()
The elliptic curves in class 142912bn have rank \(1\).
Complex multiplication
The elliptic curves in class 142912bn do not have complex multiplication.Modular form 142912.2.a.bn
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 Cremona 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 Cremona labels.