Properties

Label 75150i
Number of curves 2
Conductor 75150
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("75150.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75150i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.h2 75150i1 [1, -1, 0, -1207692, 1130571216] [2] 2903040 \(\Gamma_0(N)\)-optimal
75150.h1 75150i2 [1, -1, 0, -25255692, 48817755216] [2] 5806080  

Rank

sage: E.rank()
 

The elliptic curves in class 75150i have rank \(2\).

Modular form 75150.2.a.h

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

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.