Properties

 Label 4368.x Number of curves $4$ Conductor $4368$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("x1")

E.isogeny_class()

Elliptic curves in class 4368.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.x1 4368f3 $$[0, 1, 0, -952, 10868]$$ $$46640233586/599781$$ $$1228351488$$ $$[2]$$ $$2560$$ $$0.55255$$
4368.x2 4368f2 $$[0, 1, 0, -112, -220]$$ $$153091012/74529$$ $$76317696$$ $$[2, 2]$$ $$1280$$ $$0.20598$$
4368.x3 4368f1 $$[0, 1, 0, -92, -372]$$ $$340062928/273$$ $$69888$$ $$[2]$$ $$640$$ $$-0.14060$$ $$\Gamma_0(N)$$-optimal
4368.x4 4368f4 $$[0, 1, 0, 408, -1260]$$ $$3658553134/2528253$$ $$-5177862144$$ $$[2]$$ $$2560$$ $$0.55255$$

Rank

sage: E.rank()

The elliptic curves in class 4368.x have rank $$0$$.

Complex multiplication

The elliptic curves in class 4368.x do not have complex multiplication.

Modular form4368.2.a.x

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.