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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 250096bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250096.bt1 | 250096bt1 | \([0, 1, 0, -49653, 6400547]\) | \(-28094464000/20657483\) | \(-9954640762744832\) | \([]\) | \(1161216\) | \(1.7692\) | \(\Gamma_0(N)\)-optimal |
| 250096.bt2 | 250096bt2 | \([0, 1, 0, 405067, -98912605]\) | \(15252992000000/17621717267\) | \(-8491734690796679168\) | \([]\) | \(3483648\) | \(2.3185\) |
Rank
sage: E.rank()
The elliptic curves in class 250096bt have rank \(1\).
Complex multiplication
The elliptic curves in class 250096bt do not have complex multiplication.Modular form 250096.2.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.
