Properties

Label 31878.c
Number of curves $4$
Conductor $31878$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 31878.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31878.c1 31878g4 \([1, -1, 0, -86272758, -308409484460]\) \(97413070452067229637409633/140666577176907936\) \(102545934761965885344\) \([2]\) \(2949120\) \(3.1104\)  
31878.c2 31878g3 \([1, -1, 0, -13820598, 13345463956]\) \(400476194988122984445793/126270124548858769248\) \(92050920796118042781792\) \([2]\) \(2949120\) \(3.1104\)  
31878.c3 31878g2 \([1, -1, 0, -5441238, -4725463820]\) \(24439335640029940889953/902916953746891776\) \(658226459281484104704\) \([2, 2]\) \(1474560\) \(2.7639\)  
31878.c4 31878g1 \([1, -1, 0, 134442, -263804684]\) \(368637286278891167/41443067603976192\) \(-30211996283298643968\) \([2]\) \(737280\) \(2.4173\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 31878.c have rank \(1\).

Complex multiplication

The elliptic curves in class 31878.c do not have complex multiplication.

Modular form 31878.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.