Properties

Label 660.c
Number of curves $4$
Conductor $660$
CM no
Rank $1$
Graph

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

Elliptic curves in class 660.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
660.c1 660c4 \([0, 1, 0, -1556, -13356]\) \(1628514404944/664335375\) \(170069856000\) \([2]\) \(864\) \(0.85261\)  
660.c2 660c2 \([0, 1, 0, -716, 7140]\) \(158792223184/16335\) \(4181760\) \([6]\) \(288\) \(0.30330\)  
660.c3 660c1 \([0, 1, 0, -41, 120]\) \(-488095744/200475\) \(-3207600\) \([6]\) \(144\) \(-0.043272\) \(\Gamma_0(N)\)-optimal
660.c4 660c3 \([0, 1, 0, 319, -1356]\) \(223673040896/187171875\) \(-2994750000\) \([2]\) \(432\) \(0.50603\)  

Rank

sage: E.rank()
 

The elliptic curves in class 660.c have rank \(1\).

Complex multiplication

The elliptic curves in class 660.c do not have complex multiplication.

Modular form 660.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.