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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 157170.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 157170.bj1 | 157170bz4 | \([1, 0, 1, -107394603, -428381642102]\) | \(28379906689597370652529/1357352437500\) | \(6551680961496937500\) | \([2]\) | \(18662400\) | \(3.0878\) | |
| 157170.bj2 | 157170bz3 | \([1, 0, 1, -6701023, -6717206494]\) | \(-6894246873502147249/47925198774000\) | \(-231325780769132166000\) | \([2]\) | \(9331200\) | \(2.7412\) | |
| 157170.bj3 | 157170bz2 | \([1, 0, 1, -1441743, -478943294]\) | \(68663623745397169/19216056254400\) | \(92752233273244209600\) | \([2]\) | \(6220800\) | \(2.5385\) | |
| 157170.bj4 | 157170bz1 | \([1, 0, 1, 234737, -49093822]\) | \(296354077829711/387386634240\) | \(-1869841292629340160\) | \([2]\) | \(3110400\) | \(2.1919\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 157170.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 157170.bj do not have complex multiplication.Modular form 157170.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
