Properties

Label 2394.d
Number of curves $4$
Conductor $2394$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2394.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.d1 2394a4 \([1, -1, 0, -11922, 364940]\) \(9521387989875/2634569336\) \(51856228240488\) \([2]\) \(6912\) \(1.3390\)  
2394.d2 2394a2 \([1, -1, 0, -10977, 445419]\) \(5417927574172875/247646\) \(6686442\) \([6]\) \(2304\) \(0.78973\)  
2394.d3 2394a3 \([1, -1, 0, -4362, -105292]\) \(466385893875/21509824\) \(423377865792\) \([2]\) \(3456\) \(0.99246\)  
2394.d4 2394a1 \([1, -1, 0, -687, 7065]\) \(1329185824875/8941324\) \(241415748\) \([6]\) \(1152\) \(0.44316\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2394.d have rank \(1\).

Complex multiplication

The elliptic curves in class 2394.d do not have complex multiplication.

Modular form 2394.2.a.d

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.