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Properties

Label 215950s
Number of curves $2$
Conductor $215950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 215950s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215950.b2 215950s1 \([1, 1, 0, 2000, 800000]\) \(56578878719/17690624000\) \(-276416000000000\) \([]\) \(607680\) \(1.4502\) \(\Gamma_0(N)\)-optimal
215950.b1 215950s2 \([1, 1, 0, -18000, -21620000]\) \(-41281826100481/12890495001440\) \(-201413984397500000\) \([]\) \(1823040\) \(1.9995\)  

Rank

sage: E.rank()
 

The elliptic curves in class 215950s have rank \(0\).

Complex multiplication

The elliptic curves in class 215950s do not have complex multiplication.

Modular form 215950.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.