Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1936.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1936.k1 | 1936i2 | \([0, -1, 0, -832, -9216]\) | \(-128667913/4096\) | \(-2030043136\) | \([]\) | \(1152\) | \(0.56194\) | |
| 1936.k2 | 1936i1 | \([0, -1, 0, 48, -64]\) | \(24167/16\) | \(-7929856\) | \([]\) | \(384\) | \(0.012633\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1936.k have rank \(1\).
Complex multiplication
The elliptic curves in class 1936.k do not have complex multiplication.Modular form 1936.2.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 LMFDB 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 LMFDB labels.
