Properties

Label 30767d
Number of curves 11
Conductor 3076730767
CM no
Rank 33

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 30767d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30767.a1 30767d1 [0,0,1,31,60][0, 0, 1, -31, 60] 3294646272/3384373294646272/338437 338437338437 [][] 1363213632 0.20347-0.20347 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 30767d1 has rank 33.

Complex multiplication

The elliptic curves in class 30767d do not have complex multiplication.

Modular form 30767.2.a.d

sage: E.q_eigenform(10)
 
q2q23q3+2q42q5+6q63q7+6q9+4q10+q116q126q13+6q14+6q154q165q1712q184q19+O(q20)q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 2 q^{5} + 6 q^{6} - 3 q^{7} + 6 q^{9} + 4 q^{10} + q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 4 q^{16} - 5 q^{17} - 12 q^{18} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display