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Properties

Label 386575.c
Number of curves $2$
Conductor $386575$
CM no
Rank $0$
Graph

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

Elliptic curves in class 386575.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
386575.c1 386575c2 \([1, -1, 1, -95549605, 359271339772]\) \(5517084663/4375\) \(76503059684759462890625\) \([2]\) \(51111936\) \(3.3214\)  
386575.c2 386575c1 \([1, -1, 1, -4704480, 8064086522]\) \(-658503/1225\) \(-21420856711732649609375\) \([2]\) \(25555968\) \(2.9748\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 386575.c have rank \(0\).

Complex multiplication

The elliptic curves in class 386575.c do not have complex multiplication.

Modular form 386575.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3 q^{8} - 3 q^{9} + 6 q^{11} + 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + 3 q^{18} + 8 q^{19} + O(q^{20})\) 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.