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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 70560.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.bs1 | 70560dj4 | \([0, 0, 0, -165963, -26017922]\) | \(11512557512/2835\) | \(124491239953920\) | \([2]\) | \(393216\) | \(1.6925\) | |
70560.bs2 | 70560dj3 | \([0, 0, 0, -77763, 8124298]\) | \(1184287112/36015\) | \(1581499826081280\) | \([2]\) | \(393216\) | \(1.6925\) | |
70560.bs3 | 70560dj1 | \([0, 0, 0, -11613, -303212]\) | \(31554496/11025\) | \(60516574977600\) | \([2, 2]\) | \(196608\) | \(1.3460\) | \(\Gamma_0(N)\)-optimal |
70560.bs4 | 70560dj2 | \([0, 0, 0, 34692, -2118368]\) | \(13144256/13125\) | \(-4610786664960000\) | \([2]\) | \(393216\) | \(1.6925\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 70560.bs do not have complex multiplication.Modular form 70560.2.a.bs
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.