Properties

Label 271950p
Number of curves $2$
Conductor $271950$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 271950p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271950.p1 271950p1 \([1, 1, 0, -13500, -1144800]\) \(-3700897225/5482512\) \(-403132533930000\) \([]\) \(1824768\) \(1.4943\) \(\Gamma_0(N)\)-optimal
271950.p2 271950p2 \([1, 1, 0, 115125, 22753725]\) \(2294872120775/4356968448\) \(-320370613086720000\) \([]\) \(5474304\) \(2.0436\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271950p have rank \(2\).

Complex multiplication

The elliptic curves in class 271950p do not have complex multiplication.

Modular form 271950.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 3 q^{11} - q^{12} - 5 q^{13} + q^{16} + 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.