Properties

 Label 4560.g Number of curves $2$ Conductor $4560$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 4560.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.g1 4560b2 $$[0, -1, 0, -96, 96]$$ $$48275138/27075$$ $$55449600$$ $$$$ $$1280$$ $$0.17609$$
4560.g2 4560b1 $$[0, -1, 0, 24, 0]$$ $$1431644/855$$ $$-875520$$ $$$$ $$640$$ $$-0.17048$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 4560.g have rank $$1$$.

Complex multiplication

The elliptic curves in class 4560.g do not have complex multiplication.

Modular form4560.2.a.g

sage: E.q_eigenform(10)

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