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Properties

Label 1230k
Number of curves $2$
Conductor $1230$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1230k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1230.k2 1230k1 \([1, 0, 0, 2305, -15975]\) \(1354330706847119/896670000000\) \(-896670000000\) \([7]\) \(1960\) \(0.98228\) \(\Gamma_0(N)\)-optimal
1230.k1 1230k2 \([1, 0, 0, -1202045, -507358545]\) \(-192081665892474305747281/5842628216430\) \(-5842628216430\) \([]\) \(13720\) \(1.9552\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1230k have rank \(0\).

Complex multiplication

The elliptic curves in class 1230k do not have complex multiplication.

Modular form 1230.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.