Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 463680.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.h1 | 463680h1 | \([0, 0, 0, -363648, 84400472]\) | \(7124261256822784/475453125\) | \(354923856000000\) | \([2]\) | \(4423680\) | \(1.8475\) | \(\Gamma_0(N)\)-optimal |
463680.h2 | 463680h2 | \([0, 0, 0, -341148, 95299472]\) | \(-367624742361424/115740505125\) | \(-1382397185820672000\) | \([2]\) | \(8847360\) | \(2.1941\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.h have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.h do not have complex multiplication.Modular form 463680.2.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.