# Properties

 Label 4275f Number of curves $2$ Conductor $4275$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 4275f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4275.o2 4275f1 $$[1, -1, 0, 333, 59616]$$ $$357911/135375$$ $$-1542005859375$$ $$[2]$$ $$4608$$ $$1.0178$$ $$\Gamma_0(N)$$-optimal
4275.o1 4275f2 $$[1, -1, 0, -21042, 1149741]$$ $$90458382169/2671875$$ $$30434326171875$$ $$[2]$$ $$9216$$ $$1.3644$$

## Rank

sage: E.rank()

The elliptic curves in class 4275f have rank $$0$$.

## Complex multiplication

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

## Modular form4275.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 2 q^{7} - 3 q^{8} + 2 q^{11} + 4 q^{13} + 2 q^{14} - q^{16} + 2 q^{17} - q^{19} + O(q^{20})$$

## 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 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.