# Properties

 Label 14400fi Number of curves 2 Conductor 14400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.l1")

sage: E.isogeny_class()

## Elliptic curves in class 14400fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.l2 14400fi1 [0, 0, 0, -1155, -17800]  12288 $$\Gamma_0(N)$$-optimal
14400.l1 14400fi2 [0, 0, 0, -19380, -1038400]  24576

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.l

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. 