Properties

Label 215475k
Number of curves $2$
Conductor $215475$
CM no
Rank $1$
Graph

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

Elliptic curves in class 215475k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215475.u1 215475k1 \([1, 0, 0, -6068, -176073]\) \(89975616641/3581577\) \(983590583625\) \([2]\) \(304128\) \(1.0678\) \(\Gamma_0(N)\)-optimal
215475.u2 215475k2 \([1, 0, 0, 2707, -641148]\) \(7988005999/651714363\) \(-178977056938875\) \([2]\) \(608256\) \(1.4144\)  

Rank

sage: E.rank()
 

The elliptic curves in class 215475k have rank \(1\).

Complex multiplication

The elliptic curves in class 215475k do not have complex multiplication.

Modular form 215475.2.a.k

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