Properties

Label 8036.c
Number of curves $2$
Conductor $8036$
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 8036.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8036.c1 8036f1 \([0, -1, 0, -44, -104]\) \(-768208/41\) \(-514304\) \([]\) \(1152\) \(-0.14519\) \(\Gamma_0(N)\)-optimal
8036.c2 8036f2 \([0, -1, 0, 236, -328]\) \(115393712/68921\) \(-864545024\) \([]\) \(3456\) \(0.40411\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8036.c have rank \(0\).

Complex multiplication

The elliptic curves in class 8036.c do not have complex multiplication.

Modular form 8036.2.a.c

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.