Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1550.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1550.a1 | 1550c2 | \([1, 0, 1, -26651, -1676802]\) | \(133974081659809/192200\) | \(3003125000\) | \([2]\) | \(2304\) | \(1.0897\) | |
1550.a2 | 1550c1 | \([1, 0, 1, -1651, -26802]\) | \(-31824875809/1240000\) | \(-19375000000\) | \([2]\) | \(1152\) | \(0.74308\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1550.a have rank \(1\).
Complex multiplication
The elliptic curves in class 1550.a do not have complex multiplication.Modular form 1550.2.a.a
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.