Properties

Label 2352.q
Number of curves $4$
Conductor $2352$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 2352.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2352.q1 2352i3 \([0, 1, 0, -7464, 245412]\) \(381775972/567\) \(68307950592\) \([4]\) \(3072\) \(0.97991\)  
2352.q2 2352i2 \([0, 1, 0, -604, 1196]\) \(810448/441\) \(13282101504\) \([2, 2]\) \(1536\) \(0.63334\)  
2352.q3 2352i1 \([0, 1, 0, -359, -2724]\) \(2725888/21\) \(39530064\) \([2]\) \(768\) \(0.28677\) \(\Gamma_0(N)\)-optimal
2352.q4 2352i4 \([0, 1, 0, 2336, 11780]\) \(11696828/7203\) \(-867763964928\) \([2]\) \(3072\) \(0.97991\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2352.q have rank \(1\).

Complex multiplication

The elliptic curves in class 2352.q do not have complex multiplication.

Modular form 2352.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.