Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 115920.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.bv1 | 115920dt1 | \([0, 0, 0, -743763, -246711278]\) | \(15238420194810961/12619514880\) | \(37681669519441920\) | \([2]\) | \(1290240\) | \(2.1090\) | \(\Gamma_0(N)\)-optimal |
115920.bv2 | 115920dt2 | \([0, 0, 0, -582483, -356671982]\) | \(-7319577278195281/14169067365600\) | \(-42308608448603750400\) | \([2]\) | \(2580480\) | \(2.4556\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.bv do not have complex multiplication.Modular form 115920.2.a.bv
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.