Properties

Label 2415.c
Number of curves $4$
Conductor $2415$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2415.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2415.c1 2415h3 \([1, 0, 0, -4430, -113505]\) \(9614816895690721/34652610405\) \(34652610405\) \([2]\) \(2048\) \(0.88359\)  
2415.c2 2415h2 \([1, 0, 0, -405, 0]\) \(7347774183121/4251692025\) \(4251692025\) \([2, 2]\) \(1024\) \(0.53702\)  
2415.c3 2415h1 \([1, 0, 0, -280, 1775]\) \(2428257525121/8150625\) \(8150625\) \([4]\) \(512\) \(0.19044\) \(\Gamma_0(N)\)-optimal
2415.c4 2415h4 \([1, 0, 0, 1620, 405]\) \(470166844956479/272118787605\) \(-272118787605\) \([2]\) \(2048\) \(0.88359\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2415.c have rank \(1\).

Complex multiplication

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

Modular form 2415.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.