Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 123840bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.m2 | 123840bt1 | \([0, 0, 0, -3423, -81668]\) | \(-95068558144/6739605\) | \(-314443010880\) | \([2]\) | \(233472\) | \(0.95637\) | \(\Gamma_0(N)\)-optimal |
| 123840.m1 | 123840bt2 | \([0, 0, 0, -55668, -5055392]\) | \(6389297223616/29025\) | \(86668185600\) | \([2]\) | \(466944\) | \(1.3029\) |
Rank
sage: E.rank()
The elliptic curves in class 123840bt have rank \(0\).
Complex multiplication
The elliptic curves in class 123840bt do not have complex multiplication.Modular form 123840.2.a.bt
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.
