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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 155526.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.bu1 | 155526bf4 | \([1, 1, 1, -4635945469, -121496144555899]\) | \(632678989847546725777/80515134\) | \(1402273659444691779774\) | \([2]\) | \(97320960\) | \(3.9177\) | |
155526.bu2 | 155526bf3 | \([1, 1, 1, -331504209, -1315720094403]\) | \(231331938231569617/90942310746882\) | \(1583876229894699585347881602\) | \([2]\) | \(97320960\) | \(3.9177\) | |
155526.bu3 | 155526bf2 | \([1, 1, 1, -289771399, -1898126497639]\) | \(154502321244119857/55101928644\) | \(959670303996291717202884\) | \([2, 2]\) | \(48660480\) | \(3.5711\) | |
155526.bu4 | 155526bf1 | \([1, 1, 1, -15527219, -38421864223]\) | \(-23771111713777/22848457968\) | \(-397935011416059822379248\) | \([2]\) | \(24330240\) | \(3.2245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 155526.bu do not have complex multiplication.Modular form 155526.2.a.bu
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.