Properties

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

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

sage: E.isogeny_class()

Elliptic curves in class 4560.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.t1 4560w2 $$[0, 1, 0, -31976, 2185524]$$ $$882774443450089/2166000000$$ $$8871936000000$$ $$$$ $$16128$$ $$1.3627$$
4560.t2 4560w1 $$[0, 1, 0, -1256, 59700]$$ $$-53540005609/350208000$$ $$-1434451968000$$ $$$$ $$8064$$ $$1.0161$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form4560.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 2 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - q^{15} + 4 q^{17} - q^{19} + O(q^{20})$$ 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. 