Properties

Label 114.c
Number of curves $4$
Conductor $114$
CM no
Rank $0$
Graph

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

Elliptic curves in class 114.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114.c1 114a3 \([1, 0, 0, -428, -3444]\) \(8671983378625/82308\) \(82308\) \([2]\) \(36\) \(0.10550\)  
114.c2 114a4 \([1, 0, 0, -418, -3610]\) \(-8078253774625/846825858\) \(-846825858\) \([2]\) \(72\) \(0.45208\)  
114.c3 114a1 \([1, 0, 0, -8, 0]\) \(57066625/32832\) \(32832\) \([6]\) \(12\) \(-0.44380\) \(\Gamma_0(N)\)-optimal
114.c4 114a2 \([1, 0, 0, 32, 8]\) \(3616805375/2105352\) \(-2105352\) \([6]\) \(24\) \(-0.097231\)  

Rank

sage: E.rank()
 

The elliptic curves in class 114.c have rank \(0\).

Complex multiplication

The elliptic curves in class 114.c do not have complex multiplication.

Modular form 114.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{12} - 4q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.