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Properties

Label 15210bj
Number of curves $2$
Conductor $15210$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 15210bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bi1 15210bj1 \([1, -1, 1, -1279193, 557111481]\) \(65787589563409/10400000\) \(36594935114400000\) \([2]\) \(322560\) \(2.1887\) \(\Gamma_0(N)\)-optimal
15210.bi2 15210bj2 \([1, -1, 1, -1157513, 667256217]\) \(-48743122863889/26406250000\) \(-92916827438906250000\) \([2]\) \(645120\) \(2.5353\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15210bj have rank \(1\).

Complex multiplication

The elliptic curves in class 15210bj do not have complex multiplication.

Modular form 15210.2.a.bj

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