# Properties

 Label 14400.h Number of curves 2 Conductor 14400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.h1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.h1 14400co1 [0, 0, 0, -480, -3800]  6144 $$\Gamma_0(N)$$-optimal
14400.h2 14400co2 [0, 0, 0, 420, -16400]  12288

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.h

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 