# Properties

 Label 9408.g Number of curves $4$ Conductor $9408$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 9408.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.g1 9408ce3 $$[0, -1, 0, -43969, -3534047]$$ $$2438569736/21$$ $$80957571072$$ $$[2]$$ $$24576$$ $$1.2609$$
9408.g2 9408ce2 $$[0, -1, 0, -2809, -51911]$$ $$5088448/441$$ $$212513624064$$ $$[2, 2]$$ $$12288$$ $$0.91432$$
9408.g3 9408ce1 $$[0, -1, 0, -604, 4978]$$ $$3241792/567$$ $$4269246912$$ $$[2]$$ $$6144$$ $$0.56775$$ $$\Gamma_0(N)$$-optimal
9408.g4 9408ce4 $$[0, -1, 0, 3071, -245951]$$ $$830584/7203$$ $$-27768446877696$$ $$[2]$$ $$24576$$ $$1.2609$$

## Rank

sage: E.rank()

The elliptic curves in class 9408.g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9408.g do not have complex multiplication.

## Modular form9408.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{5} + q^{9} - 4 q^{11} - 6 q^{13} + 2 q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.