Properties

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

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

Elliptic curves in class 2394.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.h1 2394k3 \([1, -1, 1, -56516, -5157169]\) \(27384399945278713/153257496\) \(111724714584\) \([2]\) \(6144\) \(1.3122\)  
2394.h2 2394k2 \([1, -1, 1, -3596, -76849]\) \(7052482298233/499254336\) \(363956410944\) \([2, 2]\) \(3072\) \(0.96561\)  
2394.h3 2394k1 \([1, -1, 1, -716, 6095]\) \(55611739513/11440128\) \(8339853312\) \([4]\) \(1536\) \(0.61903\) \(\Gamma_0(N)\)-optimal
2394.h4 2394k4 \([1, -1, 1, 3244, -339505]\) \(5180411077127/70976229912\) \(-51741671605848\) \([2]\) \(6144\) \(1.3122\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2394.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.