Show commands:
SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 408980bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
408980.bf2 | 408980bf1 | \([0, 1, 0, 620, 41380]\) | \(176/5\) | \(-747576177920\) | \([]\) | \(331776\) | \(0.95842\) | \(\Gamma_0(N)\)-optimal* |
408980.bf1 | 408980bf2 | \([0, 1, 0, -73740, 7685588]\) | \(-296587984/125\) | \(-18689404448000\) | \([]\) | \(995328\) | \(1.5077\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 408980bf have rank \(0\).
Complex multiplication
The elliptic curves in class 408980bf do not have complex multiplication.Modular form 408980.2.a.bf
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.