Properties

 Label 346560.ev Number of curves $2$ Conductor $346560$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("ev1")

sage: E.isogeny_class()

Elliptic curves in class 346560.ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.ev1 346560ev2 $$[0, -1, 0, -84237665, 297610425825]$$ $$781484460931/900$$ $$76131579461920358400$$ $$$$ $$28016640$$ $$3.0989$$
346560.ev2 346560ev1 $$[0, -1, 0, -5221985, 4730906337]$$ $$-186169411/6480$$ $$-548147372125826580480$$ $$$$ $$14008320$$ $$2.7524$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 346560.ev have rank $$0$$.

Complex multiplication

The elliptic curves in class 346560.ev do not have complex multiplication.

Modular form 346560.2.a.ev

sage: E.q_eigenform(10)

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