# Properties

 Label 30400g Number of curves $3$ Conductor $30400$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 30400g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30400.k3 30400g1 $$[0, 1, 0, 67, 13]$$ $$32768/19$$ $$-19000000$$ $$[]$$ $$5184$$ $$0.086119$$ $$\Gamma_0(N)$$-optimal
30400.k2 30400g2 $$[0, 1, 0, -933, -11987]$$ $$-89915392/6859$$ $$-6859000000$$ $$[]$$ $$15552$$ $$0.63543$$
30400.k1 30400g3 $$[0, 1, 0, -76933, -8238987]$$ $$-50357871050752/19$$ $$-19000000$$ $$[]$$ $$46656$$ $$1.1847$$

## Rank

sage: E.rank()

The elliptic curves in class 30400g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 30400g do not have complex multiplication.

## Modular form 30400.2.a.g

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} - 3q^{11} - 4q^{13} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 