Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1792.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1792.f1 | 1792e2 | \([0, -1, 0, -29, 5]\) | \(85184/49\) | \(1605632\) | \([2]\) | \(256\) | \(-0.11964\) | |
1792.f2 | 1792e1 | \([0, -1, 0, -19, 39]\) | \(1560896/7\) | \(3584\) | \([2]\) | \(128\) | \(-0.46622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1792.f have rank \(0\).
Complex multiplication
The elliptic curves in class 1792.f do not have complex multiplication.Modular form 1792.2.a.f
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.