Properties

Label 240.c
Number of curves $6$
Conductor $240$
CM no
Rank $0$
Graph

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

Elliptic curves in class 240.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
240.c1 240a5 \([0, -1, 0, -3200, 70752]\) \(1770025017602/75\) \(153600\) \([4]\) \(128\) \(0.48000\)  
240.c2 240a3 \([0, -1, 0, -200, 1152]\) \(868327204/5625\) \(5760000\) \([2, 4]\) \(64\) \(0.13343\)  
240.c3 240a6 \([0, -1, 0, -80, 2400]\) \(-27995042/1171875\) \(-2400000000\) \([4]\) \(128\) \(0.48000\)  
240.c4 240a2 \([0, -1, 0, -20, 0]\) \(3631696/2025\) \(518400\) \([2, 2]\) \(32\) \(-0.21315\)  
240.c5 240a1 \([0, -1, 0, -15, -18]\) \(24918016/45\) \(720\) \([2]\) \(16\) \(-0.55972\) \(\Gamma_0(N)\)-optimal
240.c6 240a4 \([0, -1, 0, 80, -80]\) \(54607676/32805\) \(-33592320\) \([2]\) \(64\) \(0.13343\)  

Rank

sage: E.rank()
 

The elliptic curves in class 240.c have rank \(0\).

Complex multiplication

The elliptic curves in class 240.c do not have complex multiplication.

Modular form 240.2.a.c

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.