Properties

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

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

Elliptic curves in class 4560.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.z1 4560h2 $$[0, 1, 0, -73520, -4749132]$$ $$21459330184836962/7710029296875$$ $$15790140000000000$$ $$$$ $$26880$$ $$1.8089$$
4560.z2 4560h1 $$[0, 1, 0, 13960, -515100]$$ $$293798043977756/283988784375$$ $$-290804515200000$$ $$$$ $$13440$$ $$1.4624$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form4560.2.a.z

sage: E.q_eigenform(10)

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