Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 152400.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152400.bw1 | 152400x2 | \([0, 1, 0, -8944442408, 325592230699188]\) | \(1236526859255318155975783969/38367061931916216\) | \(2455491963642637824000000\) | \([]\) | \(86929920\) | \(4.1843\) | |
| 152400.bw2 | 152400x1 | \([0, 1, 0, -40778408, -99296692812]\) | \(117174888570509216929/1273887851544576\) | \(81528822498852864000000\) | \([]\) | \(12418560\) | \(3.2114\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152400.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 152400.bw do not have complex multiplication.Modular form 152400.2.a.bw
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
