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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 76230k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76230.bw1 76230k1 \([1, -1, 0, -2532129, -1550045315]\) \(37537160298467283/5519360000\) \(264002838865920000\) \([2]\) \(1720320\) \(2.3571\) \(\Gamma_0(N)\)-optimal
76230.bw2 76230k2 \([1, -1, 0, -2299809, -1846160387]\) \(-28124139978713043/14526050000000\) \(-694812158929350000000\) \([2]\) \(3440640\) \(2.7037\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 76230.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + 4 q^{13} + q^{14} + q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.