Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 116886t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.v2 | 116886t1 | \([1, 0, 1, -19121, -1475476]\) | \(-52802213121625/33540304392\) | \(-491063596603272\) | \([3]\) | \(601344\) | \(1.5204\) | \(\Gamma_0(N)\)-optimal |
116886.v1 | 116886t2 | \([1, 0, 1, -1734296, -879233434]\) | \(-39402364010111991625/3532128768\) | \(-51713897292288\) | \([]\) | \(1804032\) | \(2.0697\) |
Rank
sage: E.rank()
The elliptic curves in class 116886t have rank \(0\).
Complex multiplication
The elliptic curves in class 116886t do not have complex multiplication.Modular form 116886.2.a.t
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.