Properties

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

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

Elliptic curves in class 3192.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.h1 3192j3 \([0, -1, 0, -3232, -57620]\) \(1823652903746/328593657\) \(672959809536\) \([2]\) \(5120\) \(0.98860\)  
3192.h2 3192j2 \([0, -1, 0, -952, 10780]\) \(93280467172/7800849\) \(7988069376\) \([2, 2]\) \(2560\) \(0.64202\)  
3192.h3 3192j1 \([0, -1, 0, -932, 11268]\) \(350104249168/2793\) \(715008\) \([4]\) \(1280\) \(0.29545\) \(\Gamma_0(N)\)-optimal
3192.h4 3192j4 \([0, -1, 0, 1008, 47628]\) \(55251546334/517244049\) \(-1059315812352\) \([2]\) \(5120\) \(0.98860\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3192.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.