Properties

Label 21294j
Number of curves $2$
Conductor $21294$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 21294j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.v2 21294j1 \([1, -1, 0, -512862, -59250996]\) \(677353174875/322828856\) \(7110218217541099752\) \([3]\) \(404352\) \(2.3113\) \(\Gamma_0(N)\)-optimal
21294.v1 21294j2 \([1, -1, 0, -34423557, -77729060395]\) \(280965399667875/175616\) \(2819695374865893888\) \([]\) \(1213056\) \(2.8606\)  

Rank

sage: E.rank()
 

The elliptic curves in class 21294j have rank \(0\).

Complex multiplication

The elliptic curves in class 21294j do not have complex multiplication.

Modular form 21294.2.a.j

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