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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 257600bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.bw1 | 257600bw1 | \([0, -1, 0, -263281033, -1644198676063]\) | \(-126142795384287538429696/9315359375\) | \(-149045750000000000\) | \([]\) | \(27205632\) | \(3.1915\) | \(\Gamma_0(N)\)-optimal |
| 257600.bw2 | 257600bw2 | \([0, -1, 0, -260631033, -1678920026063]\) | \(-122372013839654770813696/5297595236711512175\) | \(-84761523787384194800000000\) | \([]\) | \(81616896\) | \(3.7408\) |
Rank
sage: E.rank()
The elliptic curves in class 257600bw have rank \(1\).
Complex multiplication
The elliptic curves in class 257600bw do not have complex multiplication.Modular form 257600.2.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 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.
