Properties

Label 71630.v
Number of curves $2$
Conductor $71630$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 71630.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71630.v1 71630x2 \([1, -1, 1, -6564370452, -204561760368501]\) \(31282608380024362517498521417844241/25809317141410280453312834380\) \(25809317141410280453312834380\) \([]\) \(183782144\) \(4.3803\)  
71630.v2 71630x1 \([1, -1, 1, -265716552, 1667217712779]\) \(2074815747201021028933709986641/5607507702833920000000\) \(5607507702833920000000\) \([7]\) \(26254592\) \(3.4073\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 71630.v have rank \(1\).

Complex multiplication

The elliptic curves in class 71630.v do not have complex multiplication.

Modular form 71630.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} + q^{10} + 5 q^{11} - 3 q^{12} - q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.