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Properties

Label 75150i
Number of curves $2$
Conductor $75150$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 75150i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75150.h2 75150i1 \([1, -1, 0, -1207692, 1130571216]\) \(-17101922279625721/38553753600000\) \(-439151349600000000000\) \([2]\) \(2903040\) \(2.6495\) \(\Gamma_0(N)\)-optimal
75150.h1 75150i2 \([1, -1, 0, -25255692, 48817755216]\) \(156406207396688718841/152178750000000\) \(1733411074218750000000\) \([2]\) \(5806080\) \(2.9961\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 75150.2.a.i

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