Properties

Label 18515i
Number of curves $3$
Conductor $18515$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18515i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18515.o2 18515i1 \([0, 1, 1, -705, -8234]\) \(-262144/35\) \(-5181256115\) \([]\) \(7920\) \(0.59660\) \(\Gamma_0(N)\)-optimal
18515.o3 18515i2 \([0, 1, 1, 4585, 21919]\) \(71991296/42875\) \(-6347038740875\) \([]\) \(23760\) \(1.1459\)  
18515.o1 18515i3 \([0, 1, 1, -69475, 7350156]\) \(-250523582464/13671875\) \(-2023928169921875\) \([]\) \(71280\) \(1.6952\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18515i have rank \(1\).

Complex multiplication

The elliptic curves in class 18515i do not have complex multiplication.

Modular form 18515.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} + q^{5} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} + 5q^{13} + q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.