Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("3150.g1")

sage: E.isogeny_class()

Elliptic curves in class 3150.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.g1 3150b3 [1, -1, 0, -23667, -1393759] [2] 6912
3150.g2 3150b4 [1, -1, 0, -16917, -2210509] [2] 13824
3150.g3 3150b1 [1, -1, 0, -1167, 13741] [2] 2304 $$\Gamma_0(N)$$-optimal
3150.g4 3150b2 [1, -1, 0, 1833, 70741] [2] 4608

Rank

sage: E.rank()

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

Modular form3150.2.a.g

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.