Properties

Label 395c
Number of curves $2$
Conductor $395$
CM no
Rank $0$
Graph

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

Elliptic curves in class 395c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
395.a1 395c1 \([0, -1, 1, -50, 156]\) \(-14102327296/246875\) \(-246875\) \([5]\) \(68\) \(-0.16783\) \(\Gamma_0(N)\)-optimal
395.a2 395c2 \([0, -1, 1, 300, -5724]\) \(2976041775104/15385281995\) \(-15385281995\) \([]\) \(340\) \(0.63689\)  

Rank

sage: E.rank()
 

The elliptic curves in class 395c have rank \(0\).

Complex multiplication

The elliptic curves in class 395c do not have complex multiplication.

Modular form 395.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{9} - 2 q^{10} - 3 q^{11} - 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{15} - 4 q^{16} - 2 q^{17} + 4 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.