# Properties

 Label 1248g Number of curves $2$ Conductor $1248$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1248g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.c2 1248g1 $$[0, -1, 0, -18, 36]$$ $$10648000/117$$ $$7488$$ $$$$ $$64$$ $$-0.44189$$ $$\Gamma_0(N)$$-optimal
1248.c1 1248g2 $$[0, -1, 0, -33, -15]$$ $$1000000/507$$ $$2076672$$ $$$$ $$128$$ $$-0.095314$$

## Rank

sage: E.rank()

The elliptic curves in class 1248g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1248g do not have complex multiplication.

## Modular form1248.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{7} + q^{9} + q^{13} + 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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. 