Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 11200k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.i2 | 11200k1 | \([0, 1, 0, 7, -17]\) | \(1280/7\) | \(-179200\) | \([]\) | \(1152\) | \(-0.30991\) | \(\Gamma_0(N)\)-optimal |
11200.i1 | 11200k2 | \([0, 1, 0, -393, -3137]\) | \(-262885120/343\) | \(-8780800\) | \([]\) | \(3456\) | \(0.23939\) |
Rank
sage: E.rank()
The elliptic curves in class 11200k have rank \(1\).
Complex multiplication
The elliptic curves in class 11200k do not have complex multiplication.Modular form 11200.2.a.k
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.