Properties

 Label 364650.ey Number of curves $4$ Conductor $364650$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("ey1")

sage: E.isogeny_class()

Elliptic curves in class 364650.ey

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.ey1 364650ey3 $$[1, 1, 1, -82380513, -287781855969]$$ $$3957101249824708884951625/772310238681366528$$ $$12067347479396352000000$$ $$[2]$$ $$65691648$$ $$3.2368$$
364650.ey2 364650ey4 $$[1, 1, 1, -73676513, -350955487969]$$ $$-2830680648734534916567625/1766676274677722124288$$ $$-27604316791839408192000000$$ $$[2]$$ $$131383296$$ $$3.5834$$
364650.ey3 364650ey1 $$[1, 1, 1, -2508138, 988967031]$$ $$111675519439697265625/37528570137307392$$ $$586383908395428000000$$ $$[2]$$ $$21897216$$ $$2.6875$$ $$\Gamma_0(N)$$-optimal
364650.ey4 364650ey2 $$[1, 1, 1, 7317862, 6845263031]$$ $$2773679829880629422375/2899504554614368272$$ $$-45304758665849504250000$$ $$[2]$$ $$43794432$$ $$3.0341$$

Rank

sage: E.rank()

The elliptic curves in class 364650.ey have rank $$1$$.

Complex multiplication

The elliptic curves in class 364650.ey do not have complex multiplication.

Modular form 364650.2.a.ey

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{11} - q^{12} - q^{13} + 4 q^{14} + q^{16} - q^{17} + q^{18} + 2 q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.