Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 47190bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.ca2 | 47190bv1 | \([1, 1, 1, 19660, 1747505]\) | \(356400829/760500\) | \(-1793219219005500\) | \([2]\) | \(228096\) | \(1.6112\) | \(\Gamma_0(N)\)-optimal |
47190.ca1 | 47190bv2 | \([1, 1, 1, -153370, 18773657]\) | \(169204136291/32906250\) | \(77591216206968750\) | \([2]\) | \(456192\) | \(1.9577\) |
Rank
sage: E.rank()
The elliptic curves in class 47190bv have rank \(1\).
Complex multiplication
The elliptic curves in class 47190bv do not have complex multiplication.Modular form 47190.2.a.bv
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.