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Properties

Label 75150y
Number of curves $2$
Conductor $75150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 75150y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75150.b1 75150y1 \([1, -1, 0, -3492, -172584]\) \(-16539745/36072\) \(-10272065625000\) \([]\) \(236160\) \(1.1855\) \(\Gamma_0(N)\)-optimal
75150.b2 75150y2 \([1, -1, 0, 30258, 3776166]\) \(10758425855/27944778\) \(-7957712172656250\) \([3]\) \(708480\) \(1.7348\)  

Rank

sage: E.rank()
 

The elliptic curves in class 75150y have rank \(0\).

Complex multiplication

The elliptic curves in class 75150y do not have complex multiplication.

Modular form 75150.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 4 q^{7} - q^{8} - 6 q^{11} - q^{13} + 4 q^{14} + q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.