Show commands:
SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 17328bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17328.bc2 | 17328bf1 | \([0, 1, 0, 113595, -16793613]\) | \(841232384/1121931\) | \(-216196023567200256\) | \([]\) | \(172800\) | \(2.0121\) | \(\Gamma_0(N)\)-optimal |
| 17328.bc1 | 17328bf2 | \([0, 1, 0, -25358565, -49159868013]\) | \(-9358714467168256/22284891\) | \(-4294296904023945216\) | \([]\) | \(864000\) | \(2.8168\) |
Rank
sage: E.rank()
The elliptic curves in class 17328bf have rank \(0\).
Complex multiplication
The elliptic curves in class 17328bf do not have complex multiplication.Modular form 17328.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
