Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 29744bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29744.v2 | 29744bi1 | \([0, 0, 0, -15379, -2227758]\) | \(-9261/44\) | \(-1911185294999552\) | \([2]\) | \(112320\) | \(1.6168\) | \(\Gamma_0(N)\)-optimal |
29744.v1 | 29744bi2 | \([0, 0, 0, -366899, -85397390]\) | \(125751501/242\) | \(10511519122497536\) | \([2]\) | \(224640\) | \(1.9634\) |
Rank
sage: E.rank()
The elliptic curves in class 29744bi have rank \(0\).
Complex multiplication
The elliptic curves in class 29744bi do not have complex multiplication.Modular form 29744.2.a.bi
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.