Properties

Label 2475h
Number of curves $3$
Conductor $2475$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2475h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2475.a3 2475h1 \([0, 0, 1, -75, -594]\) \(-4096/11\) \(-125296875\) \([]\) \(840\) \(0.24130\) \(\Gamma_0(N)\)-optimal
2475.a2 2475h2 \([0, 0, 1, -2325, 78156]\) \(-122023936/161051\) \(-1834471546875\) \([]\) \(4200\) \(1.0460\)  
2475.a1 2475h3 \([0, 0, 1, -1759575, 898379406]\) \(-52893159101157376/11\) \(-125296875\) \([]\) \(21000\) \(1.8507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2475h have rank \(0\).

Complex multiplication

The elliptic curves in class 2475h do not have complex multiplication.

Modular form 2475.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} + 2 q^{7} - q^{11} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 2 q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.