Show commands:
SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 296208.ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.ew1 | 296208ew1 | \([0, 0, 0, -157179, 11646250]\) | \(81182737/35904\) | \(189926874967965696\) | \([2]\) | \(2211840\) | \(2.0112\) | \(\Gamma_0(N)\)-optimal |
296208.ew2 | 296208ew2 | \([0, 0, 0, 539781, 86778538]\) | \(3288008303/2517768\) | \(-13318622107128594432\) | \([2]\) | \(4423680\) | \(2.3577\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.ew have rank \(0\).
Complex multiplication
The elliptic curves in class 296208.ew do not have complex multiplication.Modular form 296208.2.a.ew
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.