Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 435344.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.h1 | 435344h2 | \([0, 1, 0, -82528, -9152220]\) | \(12576878500/1127\) | \(5570369272832\) | \([2]\) | \(1228800\) | \(1.4857\) | \(\Gamma_0(N)\)-optimal* |
435344.h2 | 435344h1 | \([0, 1, 0, -4788, -165476]\) | \(-9826000/3703\) | \(-4575660474112\) | \([2]\) | \(614400\) | \(1.1391\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.h have rank \(1\).
Complex multiplication
The elliptic curves in class 435344.h do not have complex multiplication.Modular form 435344.2.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.