# Properties

 Label 3150.t Number of curves $4$ Conductor $3150$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.t1 3150o3 [1, -1, 0, -84042, -9356634] [2] 12288
3150.t2 3150o2 [1, -1, 0, -5292, -142884] [2, 2] 6144
3150.t3 3150o1 [1, -1, 0, -792, 5616] [2] 3072 $$\Gamma_0(N)$$-optimal
3150.t4 3150o4 [1, -1, 0, 1458, -487134] [2] 12288

## Rank

sage: E.rank()

The elliptic curves in class 3150.t have rank $$1$$.

## Complex multiplication

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

## Modular form3150.2.a.t

sage: E.q_eigenform(10)

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

## 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.