Properties

Label 525.c
Number of curves $2$
Conductor $525$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 525.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
525.c1 525c1 \([1, 1, 0, -450, 3375]\) \(5177717/189\) \(369140625\) \([2]\) \(240\) \(0.41350\) \(\Gamma_0(N)\)-optimal
525.c2 525c2 \([1, 1, 0, 175, 12750]\) \(300763/35721\) \(-69767578125\) \([2]\) \(480\) \(0.76007\)  

Rank

sage: E.rank()
 

The elliptic curves in class 525.c have rank \(1\).

Complex multiplication

The elliptic curves in class 525.c do not have complex multiplication.

Modular form 525.2.a.c

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.