# Properties

 Label 4275.h Number of curves $2$ Conductor $4275$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4275.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.h1 4275l2 $$[1, -1, 1, -17105, 47022]$$ $$48587168449/28048275$$ $$319487382421875$$ $$$$ $$15360$$ $$1.4727$$
4275.h2 4275l1 $$[1, -1, 1, 4270, 4272]$$ $$756058031/438615$$ $$-4996098984375$$ $$$$ $$7680$$ $$1.1261$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4275.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4275.h do not have complex multiplication.

## Modular form4275.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2 q^{7} + 3 q^{8} + 6 q^{11} - 2 q^{14} - q^{16} - 6 q^{17} + q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 