Show commands:
SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 47040.gh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.gh1 | 47040gs1 | \([0, 1, 0, -205, -925]\) | \(2725888/675\) | \(237081600\) | \([2]\) | \(12288\) | \(0.31733\) | \(\Gamma_0(N)\)-optimal |
47040.gh2 | 47040gs2 | \([0, 1, 0, 495, -5265]\) | \(2382032/3645\) | \(-20483850240\) | \([2]\) | \(24576\) | \(0.66390\) |
Rank
sage: E.rank()
The elliptic curves in class 47040.gh have rank \(1\).
Complex multiplication
The elliptic curves in class 47040.gh do not have complex multiplication.Modular form 47040.2.a.gh
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.