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Properties

Label 100450u
Number of curves $2$
Conductor $100450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 100450u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100450.a2 100450u1 \([1, -1, 0, -23707042, -40891467884]\) \(801581275315909089/70810888830976\) \(130169222813679616000000\) \([]\) \(23708160\) \(3.1755\) \(\Gamma_0(N)\)-optimal
100450.a1 100450u2 \([1, -1, 0, -11773858042, 491732492081116]\) \(98191033604529537629349729/10906239337336\) \(20048564871847547875000\) \([]\) \(165957120\) \(4.1484\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100450u have rank \(1\).

Complex multiplication

The elliptic curves in class 100450u do not have complex multiplication.

Modular form 100450.2.a.u

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