Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 121104bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121104.bz2 | 121104bt1 | \([0, 0, 0, -123627, 5777315098]\) | \(-117649/8118144\) | \(-14418902802284573884416\) | \([]\) | \(4515840\) | \(2.9308\) | \(\Gamma_0(N)\)-optimal |
| 121104.bz1 | 121104bt2 | \([0, 0, 0, -788510667, -8547281090822]\) | \(-30526075007211889/103499257854\) | \(-183828439001009872792313856\) | \([]\) | \(31610880\) | \(3.9037\) |
Rank
sage: E.rank()
The elliptic curves in class 121104bt have rank \(1\).
Complex multiplication
The elliptic curves in class 121104bt do not have complex multiplication.Modular form 121104.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
