Properties

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

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 $$[1, -1, 0, -1266264, -466264512]$$ $$63812982460681/10201800960$$ $$35897523478963810560$$ $$$$ $$10321920$$ $$2.4747$$ $$\Gamma_0(N)$$-optimal
441090.bh2 441090bh2 $$[1, -1, 0, 2262456, -2602551600]$$ $$363979050334199/1041836936400$$ $$-3665957219936853800400$$ $$$$ $$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)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4 q^{11} + q^{16} + 4 q^{17} + O(q^{20})$$ 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. 