Properties

 Label 214774.d Number of curves $2$ Conductor $214774$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 214774.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
214774.d1 214774m2 $$[1, -1, 0, -6602387, -6528145163]$$ $$2616032722429824267375/129231424$$ $$1572358735808$$ $$$$ $$2875392$$ $$2.2635$$
214774.d2 214774m1 $$[1, -1, 0, -412627, -101936331]$$ $$-638577663082635375/141954125824$$ $$-1727155848900608$$ $$$$ $$1437696$$ $$1.9169$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 214774.d have rank $$0$$.

Complex multiplication

The elliptic curves in class 214774.d do not have complex multiplication.

Modular form 214774.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} - 2 q^{13} + q^{14} + q^{16} + 3 q^{18} + 8 q^{19} + O(q^{20})$$ 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 LMFDB 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 LMFDB labels. 