Properties

Label 316050ic
Number of curves $2$
Conductor $316050$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ic1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 316050ic

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
316050.ic2 316050ic1 \([1, 0, 0, -45963, -2549583]\) \(5841725401/1857600\) \(3414762225000000\) \([2]\) \(2488320\) \(1.6844\) \(\Gamma_0(N)\)-optimal
316050.ic1 316050ic2 \([1, 0, 0, -290963, 58455417]\) \(1481933914201/53916840\) \(99113473580625000\) \([2]\) \(4976640\) \(2.0310\)  

Rank

sage: E.rank()
 

The elliptic curves in class 316050ic have rank \(1\).

Complex multiplication

The elliptic curves in class 316050ic do not have complex multiplication.

Modular form 316050.2.a.ic

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 2q^{11} + q^{12} - 2q^{13} + q^{16} - 4q^{17} + q^{18} + 6q^{19} + O(q^{20})\)  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 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.