Properties

Label 3192.c
Number of curves $4$
Conductor $3192$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3192.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.c1 3192b3 \([0, -1, 0, -20104, -1089956]\) \(877592260337188/494771571\) \(506646088704\) \([2]\) \(6144\) \(1.1928\)  
3192.c2 3192b4 \([0, -1, 0, -11744, 486588]\) \(174947951977348/2957342913\) \(3028319142912\) \([2]\) \(6144\) \(1.1928\)  
3192.c3 3192b2 \([0, -1, 0, -1484, -9996]\) \(1412791482832/631868769\) \(161758404864\) \([2, 2]\) \(3072\) \(0.84622\)  
3192.c4 3192b1 \([0, -1, 0, 321, -1332]\) \(227910944768/172414683\) \(-2758634928\) \([4]\) \(1536\) \(0.49965\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3192.c have rank \(0\).

Complex multiplication

The elliptic curves in class 3192.c do not have complex multiplication.

Modular form 3192.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - q^{7} + q^{9} - 2 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.