Properties

 Label 33930.t Number of curves $2$ Conductor $33930$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

Elliptic curves in class 33930.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33930.t1 33930y1 $$[1, -1, 1, -7493, -210499]$$ $$63812982460681/10201800960$$ $$7437112899840$$ $$[2]$$ $$61440$$ $$1.1922$$ $$\Gamma_0(N)$$-optimal
33930.t2 33930y2 $$[1, -1, 1, 13387, -1187683]$$ $$363979050334199/1041836936400$$ $$-759499126635600$$ $$[2]$$ $$122880$$ $$1.5388$$

Rank

sage: E.rank()

The elliptic curves in class 33930.t have rank $$0$$.

Complex multiplication

The elliptic curves in class 33930.t do not have complex multiplication.

Modular form 33930.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4 q^{11} - q^{13} + q^{16} + 4 q^{17} + O(q^{20})$$

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 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.