Properties

Label 1176.f
Number of curves $4$
Conductor $1176$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1176.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1176.f1 1176e3 \([0, 1, 0, -197584, -33870544]\) \(7080974546692/189\) \(22769316864\) \([2]\) \(4608\) \(1.5011\)  
1176.f2 1176e4 \([0, 1, 0, -19224, 116640]\) \(6522128932/3720087\) \(448168463834112\) \([4]\) \(4608\) \(1.5011\)  
1176.f3 1176e2 \([0, 1, 0, -12364, -530944]\) \(6940769488/35721\) \(1075850221824\) \([2, 2]\) \(2304\) \(1.1546\)  
1176.f4 1176e1 \([0, 1, 0, -359, -17130]\) \(-2725888/64827\) \(-122029307568\) \([2]\) \(1152\) \(0.80800\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1176.f have rank \(1\).

Complex multiplication

The elliptic curves in class 1176.f do not have complex multiplication.

Modular form 1176.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.