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Properties

Label 75150p
Number of curves $2$
Conductor $75150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 75150p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75150.y2 75150p1 \([1, -1, 0, -1017, 52141]\) \(-10218313/96192\) \(-1095687000000\) \([2]\) \(147456\) \(0.99260\) \(\Gamma_0(N)\)-optimal
75150.y1 75150p2 \([1, -1, 0, -28017, 1807141]\) \(213525509833/669336\) \(7624155375000\) \([2]\) \(294912\) \(1.3392\)  

Rank

sage: E.rank()
 

The elliptic curves in class 75150p have rank \(1\).

Complex multiplication

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

Modular form 75150.2.a.p

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.