Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 7800.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7800.h1 | 7800l2 | \([0, -1, 0, -5008, 136012]\) | \(434163602/7605\) | \(243360000000\) | \([2]\) | \(9216\) | \(0.98134\) | |
7800.h2 | 7800l1 | \([0, -1, 0, -8, 6012]\) | \(-4/975\) | \(-15600000000\) | \([2]\) | \(4608\) | \(0.63476\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7800.h have rank \(0\).
Complex multiplication
The elliptic curves in class 7800.h do not have complex multiplication.Modular form 7800.2.a.h
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.