Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 30800.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30800.cv1 | 30800n2 | \([0, -1, 0, -569808, -115927888]\) | \(1278763167594532/375974556419\) | \(6015592902704000000\) | \([2]\) | \(491520\) | \(2.3092\) | |
30800.cv2 | 30800n1 | \([0, -1, 0, 95692, -12109888]\) | \(24226243449392/29774625727\) | \(-119098502908000000\) | \([2]\) | \(245760\) | \(1.9627\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30800.cv have rank \(1\).
Complex multiplication
The elliptic curves in class 30800.cv do not have complex multiplication.Modular form 30800.2.a.cv
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.