↑

Properties

Label 63525be
Number of curves $2$
Conductor $63525$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 63525be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63525.q2 63525be1 \([1, 1, 1, -160388, -12780844]\) \(131872229/56133\) \(194224675025390625\) \([2]\) \(576000\) \(2.0139\) \(\Gamma_0(N)\)-optimal
63525.q1 63525be2 \([1, 1, 1, -2202263, -1258324594]\) \(341385539669/160083\) \(553899999146484375\) \([2]\) \(1152000\) \(2.3605\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63525be have rank \(0\).

Complex multiplication

The elliptic curves in class 63525be do not have complex multiplication.

Modular form 63525.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + q^{7} + 3 q^{8} + q^{9} + q^{12} - q^{14} - q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) 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 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.