Show commands:
SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 433200hv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.hv2 | 433200hv1 | \([0, 1, 0, 213592, 112459188]\) | \(129205871/729000\) | \(-6080256576000000000\) | \([]\) | \(7464960\) | \(2.2863\) | \(\Gamma_0(N)\)-optimal* |
433200.hv1 | 433200hv2 | \([0, 1, 0, -12782408, 17605075188]\) | \(-27692833539889/35156250\) | \(-293222250000000000000\) | \([]\) | \(22394880\) | \(2.8356\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200hv have rank \(1\).
Complex multiplication
The elliptic curves in class 433200hv do not have complex multiplication.Modular form 433200.2.a.hv
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 Cremona 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 Cremona labels.