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Properties

Label 190575t
Number of curves $2$
Conductor $190575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 190575t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.by1 190575t1 \([1, -1, 1, -19625, 1029152]\) \(5177717/189\) \(30510930767625\) \([2]\) \(414720\) \(1.3570\) \(\Gamma_0(N)\)-optimal
190575.by2 190575t2 \([1, -1, 1, 7600, 3642752]\) \(300763/35721\) \(-5766565915081125\) \([2]\) \(829440\) \(1.7036\)  

Rank

sage: E.rank()
 

The elliptic curves in class 190575t have rank \(1\).

Complex multiplication

The elliptic curves in class 190575t do not have complex multiplication.

Modular form 190575.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{7} + 3 q^{8} + 2 q^{13} - q^{14} - q^{16} + 4 q^{17} + 6 q^{19} + O(q^{20})\) 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.