Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 55440bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55440.d2 | 55440bw1 | \([0, 0, 0, 134877, 9934178]\) | \(2453656100384133/1805439453125\) | \(-199667160000000000\) | \([2]\) | \(512000\) | \(2.0079\) | \(\Gamma_0(N)\)-optimal |
55440.d1 | 55440bw2 | \([0, 0, 0, -615123, 84484178]\) | \(232747967939865867/106810953528125\) | \(11812436972582400000\) | \([2]\) | \(1024000\) | \(2.3545\) |
Rank
sage: E.rank()
The elliptic curves in class 55440bw have rank \(0\).
Complex multiplication
The elliptic curves in class 55440bw do not have complex multiplication.Modular form 55440.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.