Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 102960.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.bw1 | 102960bx2 | \([0, 0, 0, -360123, -83180822]\) | \(46703838741180867/148720000\) | \(16447242240000\) | \([2]\) | \(516096\) | \(1.7605\) | |
| 102960.bw2 | 102960bx1 | \([0, 0, 0, -22203, -1336598]\) | \(-10945484159427/644300800\) | \(-71254514073600\) | \([2]\) | \(258048\) | \(1.4140\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.bw do not have complex multiplication.Modular form 102960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
