Properties

Label 374850.jf
Number of curves $6$
Conductor $374850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jf1")
 
E.isogeny_class()
 

Elliptic curves in class 374850.jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374850.jf1 374850jf6 \([1, -1, 1, -19211944730, -1024949657573103]\) \(585196747116290735872321/836876053125000\) \(1121493950536268408203125000\) \([2]\) \(679477248\) \(4.4616\)  
374850.jf2 374850jf3 \([1, -1, 1, -2785135730, 56565800190897]\) \(1782900110862842086081/328139630024640\) \(439738487712320425335000000\) \([2]\) \(339738624\) \(4.1151\)  
374850.jf3 374850jf4 \([1, -1, 1, -1211647730, -15709005377103]\) \(146796951366228945601/5397929064360000\) \(7233741207551821055625000000\) \([2, 2]\) \(339738624\) \(4.1151\)  
374850.jf4 374850jf2 \([1, -1, 1, -192055730, 690112350897]\) \(584614687782041281/184812061593600\) \(247665838076502350400000000\) \([2, 2]\) \(169869312\) \(3.7685\)  
374850.jf5 374850jf1 \([1, -1, 1, 33736270, 73248606897]\) \(3168685387909439/3563732336640\) \(-4775742168685608960000000\) \([2]\) \(84934656\) \(3.4219\) \(\Gamma_0(N)\)-optimal
374850.jf6 374850jf5 \([1, -1, 1, 475177270, -56024122877103]\) \(8854313460877886399/1016927675429790600\) \(-1362780344674377306316603125000\) \([2]\) \(679477248\) \(4.4616\)  

Rank

sage: E.rank()
 

The elliptic curves in class 374850.jf have rank \(0\).

Complex multiplication

The elliptic curves in class 374850.jf do not have complex multiplication.

Modular form 374850.2.a.jf

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.