# Properties

 Label 1425.g Number of curves $2$ Conductor $1425$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1425.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1425.g1 1425c2 $$[1, 1, 0, -1900, -2375]$$ $$48587168449/28048275$$ $$438254296875$$ $$$$ $$1920$$ $$0.92336$$
1425.g2 1425c1 $$[1, 1, 0, 475, 0]$$ $$756058031/438615$$ $$-6853359375$$ $$$$ $$960$$ $$0.57679$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1425.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1425.g do not have complex multiplication.

## Modular form1425.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - 3 q^{8} + q^{9} - 6 q^{11} + q^{12} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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. 