Properties

Label 63504.i
Number of curves $2$
Conductor $63504$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 63504.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63504.i1 63504cd2 \([0, 0, 0, -43659, -3834054]\) \(-35937/4\) \(-1024385060192256\) \([]\) \(248832\) \(1.6176\)  
63504.i2 63504cd1 \([0, 0, 0, 3381, 7546]\) \(109503/64\) \(-2498119335936\) \([]\) \(82944\) \(1.0683\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 63504.i have rank \(1\).

Complex multiplication

The elliptic curves in class 63504.i do not have complex multiplication.

Modular form 63504.2.a.i

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} + q^{13} - 3 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.