Properties

Label 2304.k
Number of curves $2$
Conductor $2304$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 2304.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2304.k1 2304d1 \([0, 0, 0, -210, 1168]\) \(2744000/9\) \(3359232\) \([2]\) \(512\) \(0.11759\) \(\Gamma_0(N)\)-optimal
2304.k2 2304d2 \([0, 0, 0, -120, 2176]\) \(-8000/81\) \(-1934917632\) \([2]\) \(1024\) \(0.46417\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2304.k have rank \(0\).

Complex multiplication

The elliptic curves in class 2304.k do not have complex multiplication.

Modular form 2304.2.a.k

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} + 4 q^{11} + 4 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.