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Properties

Label 465690c
Number of curves $2$
Conductor $465690$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 465690c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
465690.c1 465690c1 \([1, 1, 0, -10202793553, 396644237892757]\) \(2496660002148802349535638689/139440550809600000000\) \(6560103559962895257600000000\) \([2]\) \(945561600\) \(4.4026\) \(\Gamma_0(N)\)-optimal
465690.c2 465690c2 \([1, 1, 0, -9625193553, 443534614532757]\) \(-2096189402176608102649238689/593373633120258765120000\) \(-27915785332313352553042470720000\) \([2]\) \(1891123200\) \(4.7492\)  

Rank

sage: E.rank()
 

The elliptic curves in class 465690c have rank \(1\).

Complex multiplication

The elliptic curves in class 465690c do not have complex multiplication.

Modular form 465690.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} + 6 q^{13} + 2 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.