Properties

 Label 14400eh Number of curves $4$ Conductor $14400$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("eh1")

sage: E.isogeny_class()

Elliptic curves in class 14400eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.g3 14400eh1 $$[0, 0, 0, -1800, 27000]$$ $$55296/5$$ $$58320000000$$ $$[2]$$ $$12288$$ $$0.80524$$ $$\Gamma_0(N)$$-optimal
14400.g2 14400eh2 $$[0, 0, 0, -6300, -162000]$$ $$148176/25$$ $$4665600000000$$ $$[2, 2]$$ $$24576$$ $$1.1518$$
14400.g1 14400eh3 $$[0, 0, 0, -96300, -11502000]$$ $$132304644/5$$ $$3732480000000$$ $$[2]$$ $$49152$$ $$1.4984$$
14400.g4 14400eh4 $$[0, 0, 0, 11700, -918000]$$ $$237276/625$$ $$-466560000000000$$ $$[2]$$ $$49152$$ $$1.4984$$

Rank

sage: E.rank()

The elliptic curves in class 14400eh have rank $$1$$.

Complex multiplication

The elliptic curves in class 14400eh do not have complex multiplication.

Modular form 14400.2.a.eh

sage: E.q_eigenform(10)

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

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 Cremona 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 Cremona labels.