Properties

Label 840c
Number of curves $4$
Conductor $840$
CM no
Rank $0$
Graph

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

Elliptic curves in class 840c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.e4 840c1 \([0, -1, 0, -15, 12]\) \(24918016/13125\) \(210000\) \([4]\) \(64\) \(-0.28715\) \(\Gamma_0(N)\)-optimal
840.e2 840c2 \([0, -1, 0, -140, -588]\) \(1193895376/11025\) \(2822400\) \([2, 2]\) \(128\) \(0.059426\)  
840.e1 840c3 \([0, -1, 0, -2240, -40068]\) \(1214399773444/105\) \(107520\) \([2]\) \(256\) \(0.40600\)  
840.e3 840c4 \([0, -1, 0, -40, -1508]\) \(-7086244/972405\) \(-995742720\) \([2]\) \(256\) \(0.40600\)  

Rank

sage: E.rank()
 

The elliptic curves in class 840c have rank \(0\).

Complex multiplication

The elliptic curves in class 840c do not have complex multiplication.

Modular form 840.2.a.c

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