Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 7098.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7098.bc1 | 7098y3 | \([1, 0, 0, -13517, 603537]\) | \(124318741396429/51631104\) | \(113433535488\) | \([2]\) | \(12000\) | \(1.0830\) | |
| 7098.bc2 | 7098y4 | \([1, 0, 0, -11437, 796145]\) | \(-75306487574989/81352871712\) | \(-178732259151264\) | \([2]\) | \(24000\) | \(1.4296\) | |
| 7098.bc3 | 7098y1 | \([1, 0, 0, -452, -3732]\) | \(4649101309/6804\) | \(14948388\) | \([2]\) | \(2400\) | \(0.27833\) | \(\Gamma_0(N)\)-optimal |
| 7098.bc4 | 7098y2 | \([1, 0, 0, -322, -5890]\) | \(-1680914269/5786802\) | \(-12713603994\) | \([2]\) | \(4800\) | \(0.62490\) |
Rank
sage: E.rank()
The elliptic curves in class 7098.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.bc do not have complex multiplication.Modular form 7098.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
