Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 7056.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.bt1 | 7056g2 | \([0, 0, 0, -5439, 154350]\) | \(21882096/7\) | \(5692329216\) | \([2]\) | \(6144\) | \(0.84666\) | |
| 7056.bt2 | 7056g1 | \([0, 0, 0, -294, 3087]\) | \(-55296/49\) | \(-2490394032\) | \([2]\) | \(3072\) | \(0.50008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.bt do not have complex multiplication.Modular form 7056.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
