Properties

Label 1040.c
Number of curves $2$
Conductor $1040$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1040.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1040.c1 1040b1 \([0, 1, 0, -20, 28]\) \(3631696/65\) \(16640\) \([2]\) \(64\) \(-0.39434\) \(\Gamma_0(N)\)-optimal
1040.c2 1040b2 \([0, 1, 0, 0, 100]\) \(-4/4225\) \(-4326400\) \([2]\) \(128\) \(-0.047762\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1040.c have rank \(1\).

Complex multiplication

The elliptic curves in class 1040.c do not have complex multiplication.

Modular form 1040.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.