Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 75150.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75150.x1 75150q2 \([1, -1, 0, -4759542, -3835054634]\) \(1046819248735488409/47650971093750\) \(542774342614746093750\) \([2]\) \(4128768\) \(2.7406\)  
75150.x2 75150q1 \([1, -1, 0, 161208, -228144884]\) \(40675641638471/1996889557500\) \(-22745820115898437500\) \([2]\) \(2064384\) \(2.3940\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 75150.2.a.x

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