Properties

Label 76230x
Number of curves $2$
Conductor $76230$
CM no
Rank $1$
Graph

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

Elliptic curves in class 76230x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76230.a1 76230x1 \([1, -1, 0, -1260, 50166]\) \(-2509090441/10718750\) \(-945490218750\) \([]\) \(155520\) \(0.98297\) \(\Gamma_0(N)\)-optimal
76230.a2 76230x2 \([1, -1, 0, 11115, -1204659]\) \(1721540467559/8070721400\) \(-711910263972600\) \([]\) \(466560\) \(1.5323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 76230x have rank \(1\).

Complex multiplication

The elliptic curves in class 76230x do not have complex multiplication.

Modular form 76230.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 5 q^{13} + q^{14} + q^{16} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.