Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2160.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2160.h1 | 2160m1 | \([0, 0, 0, -648, -6372]\) | \(-5971968/25\) | \(-125971200\) | \([]\) | \(864\) | \(0.40927\) | \(\Gamma_0(N)\)-optimal |
2160.h2 | 2160m2 | \([0, 0, 0, 1512, -33588]\) | \(8429568/15625\) | \(-708588000000\) | \([]\) | \(2592\) | \(0.95857\) |
Rank
sage: E.rank()
The elliptic curves in class 2160.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2160.h do not have complex multiplication.Modular form 2160.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.