Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 223146.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223146.bw1 | 223146dz3 | \([1, -1, 0, -4227365151, 105792907900077]\) | \(97413070452067229637409633/140666577176907936\) | \(12064426678810524444836256\) | \([2]\) | \(141557760\) | \(4.0834\) | |
| 223146.bw2 | 223146dz4 | \([1, -1, 0, -677209311, -4576139718291]\) | \(400476194988122984445793/126270124548858769248\) | \(10829698780742491615235047008\) | \([2]\) | \(141557760\) | \(4.0834\) | |
| 223146.bw3 | 223146dz2 | \([1, -1, 0, -266620671, 1621367331597]\) | \(24439335640029940889953/902916953746891776\) | \(77439684708007323434320896\) | \([2, 2]\) | \(70778880\) | \(3.7368\) | |
| 223146.bw4 | 223146dz1 | \([1, -1, 0, 6587649, 90471831309]\) | \(368637286278891167/41443067603976192\) | \(-3554411150733802164191232\) | \([2]\) | \(35389440\) | \(3.3902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 223146.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 223146.bw do not have complex multiplication.Modular form 223146.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
