Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 10944.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.bt1 | 10944bt2 | \([0, 0, 0, -158052, -24185162]\) | \(-9358714467168256/22284891\) | \(-1039723874496\) | \([]\) | \(38400\) | \(1.5473\) | |
| 10944.bt2 | 10944bt1 | \([0, 0, 0, 708, -8282]\) | \(841232384/1121931\) | \(-52344812736\) | \([]\) | \(7680\) | \(0.74257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10944.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 10944.bt do not have complex multiplication.Modular form 10944.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
