Properties

Label 5265.i
Number of curves $2$
Conductor $5265$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5265.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5265.i1 5265j2 \([0, 0, 1, -1782, -27763]\) \(1177583616/54925\) \(29189396925\) \([]\) \(3888\) \(0.76921\)  
5265.i2 5265j1 \([0, 0, 1, -282, 1812]\) \(30618648576/203125\) \(16453125\) \([3]\) \(1296\) \(0.21990\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5265.i have rank \(1\).

Complex multiplication

The elliptic curves in class 5265.i do not have complex multiplication.

Modular form 5265.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} + q^{5} - 4 q^{7} + q^{13} + 4 q^{16} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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.