Show commands:
SageMath
E = EllipticCurve("ec1")
E.isogeny_class()
Elliptic curves in class 92736ec
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.j2 | 92736ec1 | \([0, 0, 0, 1716, 120976]\) | \(2924207/34776\) | \(-6645797093376\) | \([]\) | \(184320\) | \(1.1413\) | \(\Gamma_0(N)\)-optimal |
92736.j1 | 92736ec2 | \([0, 0, 0, -15564, -3411056]\) | \(-2181825073/25039686\) | \(-4785158512705536\) | \([]\) | \(552960\) | \(1.6906\) |
Rank
sage: E.rank()
The elliptic curves in class 92736ec have rank \(1\).
Complex multiplication
The elliptic curves in class 92736ec do not have complex multiplication.Modular form 92736.2.a.ec
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.