# Properties

 Label 3150.a Number of curves $2$ Conductor $3150$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3150.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.a1 3150m2 $$[1, -1, 0, -78867, 9039541]$$ $$-7620530425/526848$$ $$-3750705000000000$$ $$[]$$ $$25920$$ $$1.7393$$
3150.a2 3150m1 $$[1, -1, 0, 5508, 11416]$$ $$2595575/1512$$ $$-10764140625000$$ $$[]$$ $$8640$$ $$1.1900$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3150.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3150.a do not have complex multiplication.

## Modular form3150.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 6q^{11} + q^{13} + q^{14} + q^{16} + 3q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.