Show commands:
SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 95370bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.bq2 | 95370bs1 | \([1, 0, 1, -6585883, -35659775194]\) | \(-1308796492121439049/22000592486400000\) | \(-531040819181361561600000\) | \([2]\) | \(14376960\) | \(3.2336\) | \(\Gamma_0(N)\)-optimal |
95370.bq1 | 95370bs2 | \([1, 0, 1, -207822363, -1148819487962]\) | \(41125104693338423360329/179205840000000000\) | \(4325593328202960000000000\) | \([2]\) | \(28753920\) | \(3.5802\) |
Rank
sage: E.rank()
The elliptic curves in class 95370bs have rank \(0\).
Complex multiplication
The elliptic curves in class 95370bs do not have complex multiplication.Modular form 95370.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.