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Properties

Label 308550ik
Number of curves $2$
Conductor $308550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ik1")
 
E.isogeny_class()
 

Elliptic curves in class 308550ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.ik2 308550ik1 \([1, 0, 0, -1245655738, 16264931301092]\) \(7722211175253055152433/340131399900069888\) \(9415055045911995482112000000\) \([2]\) \(249200640\) \(4.1308\) \(\Gamma_0(N)\)-optimal
308550.ik1 308550ik2 \([1, 0, 0, -3352023738, -53247319066908]\) \(150476552140919246594353/42832838728685592576\) \(1185640415797327766711424000000\) \([2]\) \(498401280\) \(4.4773\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308550ik have rank \(1\).

Complex multiplication

The elliptic curves in class 308550ik do not have complex multiplication.

Modular form 308550.2.a.ik

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{12} + 4 q^{13} - 2 q^{14} + q^{16} + q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.