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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 156816.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 156816.bw1 | 156816bk4 | \([0, 0, 0, -18768915, -31297317678]\) | \(-189613868625/128\) | \(-493606744569151488\) | \([]\) | \(4082400\) | \(2.7108\) | |
| 156816.bw2 | 156816bk3 | \([0, 0, 0, -183315, -61367086]\) | \(-1159088625/2097152\) | \(-1232625042374787072\) | \([]\) | \(1360800\) | \(2.1615\) | |
| 156816.bw3 | 156816bk1 | \([0, 0, 0, -9075, 348722]\) | \(-140625/8\) | \(-4702091378688\) | \([]\) | \(194400\) | \(1.1885\) | \(\Gamma_0(N)\)-optimal |
| 156816.bw4 | 156816bk2 | \([0, 0, 0, 49005, 646866]\) | \(3375/2\) | \(-7712605383892992\) | \([]\) | \(583200\) | \(1.7378\) |
Rank
sage: E.rank()
The elliptic curves in class 156816.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 156816.bw do not have complex multiplication.Modular form 156816.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
