# Properties

 Label 930a Number of curves $4$ Conductor $930$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 930a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.b3 930a1 $$[1, 1, 0, -108, -432]$$ $$141339344329/17141760$$ $$17141760$$ $$$$ $$288$$ $$0.11858$$ $$\Gamma_0(N)$$-optimal
930.b2 930a2 $$[1, 1, 0, -428, 2832]$$ $$8702409880009/1120910400$$ $$1120910400$$ $$[2, 2]$$ $$576$$ $$0.46515$$
930.b1 930a3 $$[1, 1, 0, -6628, 204952]$$ $$32208729120020809/658986840$$ $$658986840$$ $$$$ $$1152$$ $$0.81173$$
930.b4 930a4 $$[1, 1, 0, 652, 16008]$$ $$30579142915511/124675335000$$ $$-124675335000$$ $$$$ $$1152$$ $$0.81173$$

## Rank

sage: E.rank()

The elliptic curves in class 930a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 930a do not have complex multiplication.

## Modular form930.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 6q^{13} + q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 