Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 129285.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129285.h1 | 129285be1 | \([1, -1, 1, -30452, 1866206]\) | \(887503681/89505\) | \(314945160328305\) | \([2]\) | \(430080\) | \(1.5180\) | \(\Gamma_0(N)\)-optimal |
129285.h2 | 129285be2 | \([1, -1, 1, 37993, 9011864]\) | \(1723683599/10989225\) | \(-38668266906975225\) | \([2]\) | \(860160\) | \(1.8646\) |
Rank
sage: E.rank()
The elliptic curves in class 129285.h have rank \(0\).
Complex multiplication
The elliptic curves in class 129285.h do not have complex multiplication.Modular form 129285.2.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.