# Properties

 Label 4025.g Number of curves $2$ Conductor $4025$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 4025.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.g1 4025b1 $$[1, -1, 0, -4067, -98784]$$ $$476196576129/197225$$ $$3081640625$$ $$$$ $$3456$$ $$0.78270$$ $$\Gamma_0(N)$$-optimal
4025.g2 4025b2 $$[1, -1, 0, -3442, -130659]$$ $$-288673724529/311181605$$ $$-4862212578125$$ $$$$ $$6912$$ $$1.1293$$

## Rank

sage: E.rank()

The elliptic curves in class 4025.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4025.g do not have complex multiplication.

## Modular form4025.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{7} - 3 q^{8} - 3 q^{9} + 2 q^{11} - 4 q^{13} + q^{14} - q^{16} + 6 q^{17} - 3 q^{18} - 8 q^{19} + O(q^{20})$$

## 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. 