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Properties

Label 2394.f
Number of curves $2$
Conductor $2394$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2394.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.f1 2394d2 \([1, -1, 0, -29295, 1562733]\) \(3814038123905521/773540010432\) \(563910667604928\) \([2]\) \(21504\) \(1.5462\)  
2394.f2 2394d1 \([1, -1, 0, -9135, -312147]\) \(115650783909361/8339853312\) \(6079753064448\) \([2]\) \(10752\) \(1.1997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2394.f have rank \(0\).

Complex multiplication

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

Modular form 2394.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.