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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 15680.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.bw1 | 15680e3 | \([0, 0, 0, -16268, 773808]\) | \(123505992/4375\) | \(16866160640000\) | \([2]\) | \(36864\) | \(1.3087\) | |
| 15680.bw2 | 15680e2 | \([0, 0, 0, -2548, -32928]\) | \(3796416/1225\) | \(590315622400\) | \([2, 2]\) | \(18432\) | \(0.96212\) | |
| 15680.bw3 | 15680e1 | \([0, 0, 0, -2303, -42532]\) | \(179406144/35\) | \(263533760\) | \([2]\) | \(9216\) | \(0.61555\) | \(\Gamma_0(N)\)-optimal |
| 15680.bw4 | 15680e4 | \([0, 0, 0, 7252, -225008]\) | \(10941048/12005\) | \(-46280744796160\) | \([2]\) | \(36864\) | \(1.3087\) |
Rank
sage: E.rank()
The elliptic curves in class 15680.bw have rank \(2\).
Complex multiplication
The elliptic curves in class 15680.bw do not have complex multiplication.Modular form 15680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
