Properties

 Label 14400fi Number of curves $2$ Conductor $14400$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("fi1")

sage: E.isogeny_class()

Elliptic curves in class 14400fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.l2 14400fi1 $$[0, 0, 0, -1155, -17800]$$ $$-29218112/6561$$ $$-38263752000$$ $$[2]$$ $$12288$$ $$0.75082$$ $$\Gamma_0(N)$$-optimal
14400.l1 14400fi2 $$[0, 0, 0, -19380, -1038400]$$ $$2156689088/81$$ $$30233088000$$ $$[2]$$ $$24576$$ $$1.0974$$

Rank

sage: E.rank()

The elliptic curves in class 14400fi have rank $$0$$.

Complex multiplication

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

Modular form 14400.2.a.fi

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{13} + 8q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.