Properties

Label 2415.h
Number of curves $4$
Conductor $2415$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2415.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2415.h1 2415e3 \([1, 0, 1, -4294, 107927]\) \(8753151307882969/65205\) \(65205\) \([2]\) \(1408\) \(0.51833\)  
2415.h2 2415e2 \([1, 0, 1, -269, 1667]\) \(2141202151369/5832225\) \(5832225\) \([2, 2]\) \(704\) \(0.17176\)  
2415.h3 2415e4 \([1, 0, 1, -164, 3011]\) \(-483551781049/3672913125\) \(-3672913125\) \([2]\) \(1408\) \(0.51833\)  
2415.h4 2415e1 \([1, 0, 1, -24, 1]\) \(1439069689/828345\) \(828345\) \([2]\) \(352\) \(-0.17481\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2415.h have rank \(0\).

Complex multiplication

The elliptic curves in class 2415.h do not have complex multiplication.

Modular form 2415.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} + 2 q^{13} + q^{14} - q^{15} - q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.