Properties

 Label 259920.er Number of curves $2$ Conductor $259920$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("er1")

sage: E.isogeny_class()

Elliptic curves in class 259920.er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.er1 259920er2 $$[0, 0, 0, -189534747, 1004340419786]$$ $$781484460931/900$$ $$867186272308436582400$$ $$$$ $$28016640$$ $$3.3017$$
259920.er2 259920er1 $$[0, 0, 0, -11749467, 15960934154]$$ $$-186169411/6480$$ $$-6243741160620743393280$$ $$$$ $$14008320$$ $$2.9551$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 259920.er have rank $$0$$.

Complex multiplication

The elliptic curves in class 259920.er do not have complex multiplication.

Modular form 259920.2.a.er

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{7} + 2 q^{13} + 6 q^{17} + O(q^{20})$$ 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 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. 