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Properties

Label 63525ci
Number of curves $2$
Conductor $63525$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 63525ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63525.x2 63525ci1 \([1, 0, 0, -4848, 94887]\) \(75740658391/20253807\) \(3369727139625\) \([2]\) \(126720\) \(1.1121\) \(\Gamma_0(N)\)-optimal
63525.x1 63525ci2 \([1, 0, 0, -71673, 7378812]\) \(244738769070151/28588707\) \(4756446127125\) \([2]\) \(253440\) \(1.4587\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63525ci have rank \(2\).

Complex multiplication

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

Modular form 63525.2.a.ci

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{12} - 2 q^{13} - q^{14} - q^{16} - 8 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 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.