Properties

Label 441090bh
Number of curves $2$
Conductor $441090$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 441090bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
441090.bh1 441090bh1 \([1, -1, 0, -1266264, -466264512]\) \(63812982460681/10201800960\) \(35897523478963810560\) \([2]\) \(10321920\) \(2.4747\) \(\Gamma_0(N)\)-optimal
441090.bh2 441090bh2 \([1, -1, 0, 2262456, -2602551600]\) \(363979050334199/1041836936400\) \(-3665957219936853800400\) \([2]\) \(20643840\) \(2.8213\)  

Rank

sage: E.rank()
 

The elliptic curves in class 441090bh have rank \(0\).

Complex multiplication

The elliptic curves in class 441090bh do not have complex multiplication.

Modular form 441090.2.a.bh

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