Show commands:
SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 97104bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.b1 | 97104bt1 | \([0, -1, 0, -145752, -25125264]\) | \(-11984473/2646\) | \(-75603370757677056\) | \([]\) | \(1057536\) | \(1.9592\) | \(\Gamma_0(N)\)-optimal |
| 97104.b2 | 97104bt2 | \([0, -1, 0, 1033368, 152214384]\) | \(4271073047/2823576\) | \(-80677196972970049536\) | \([]\) | \(3172608\) | \(2.5085\) |
Rank
sage: E.rank()
The elliptic curves in class 97104bt have rank \(1\).
Complex multiplication
The elliptic curves in class 97104bt do not have complex multiplication.Modular form 97104.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
