Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 24990.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.bi1 | 24990bf2 | \([1, 0, 1, -25408, -1150474]\) | \(15417797707369/4080067320\) | \(480015840130680\) | \([2]\) | \(110592\) | \(1.5256\) | |
24990.bi2 | 24990bf1 | \([1, 0, 1, 3992, -115594]\) | \(59822347031/83966400\) | \(-9878562993600\) | \([2]\) | \(55296\) | \(1.1791\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24990.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 24990.bi do not have complex multiplication.Modular form 24990.2.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 LMFDB 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 LMFDB labels.