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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 25410bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25410.bu3 | 25410bt1 | \([1, 1, 1, -426, 1959]\) | \(4826809/1680\) | \(2976222480\) | \([2]\) | \(20480\) | \(0.51938\) | \(\Gamma_0(N)\)-optimal |
| 25410.bu2 | 25410bt2 | \([1, 1, 1, -2846, -58057]\) | \(1439069689/44100\) | \(78125840100\) | \([2, 2]\) | \(40960\) | \(0.86596\) | |
| 25410.bu4 | 25410bt3 | \([1, 1, 1, 784, -191641]\) | \(30080231/9003750\) | \(-15950692353750\) | \([2]\) | \(81920\) | \(1.2125\) | |
| 25410.bu1 | 25410bt4 | \([1, 1, 1, -45196, -3717097]\) | \(5763259856089/5670\) | \(10044750870\) | \([2]\) | \(81920\) | \(1.2125\) |
Rank
sage: E.rank()
The elliptic curves in class 25410bt have rank \(0\).
Complex multiplication
The elliptic curves in class 25410bt do not have complex multiplication.Modular form 25410.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
