Properties

 Label 2760.g Number of curves $2$ Conductor $2760$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

Elliptic curves in class 2760.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2760.g1 2760g2 $$[0, -1, 0, -960, -9108]$$ $$47825527682/8926875$$ $$18282240000$$ $$[2]$$ $$2304$$ $$0.68713$$
2760.g2 2760g1 $$[0, -1, 0, 120, -900]$$ $$185073116/419175$$ $$-429235200$$ $$[2]$$ $$1152$$ $$0.34056$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2760.g have rank $$0$$.

Complex multiplication

The elliptic curves in class 2760.g do not have complex multiplication.

Modular form2760.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2 q^{7} + q^{9} - 2 q^{11} + 2 q^{13} - q^{15} - 8 q^{17} + 4 q^{19} + O(q^{20})$$

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.