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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 966.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
966.j1 | 966i3 | \([1, 0, 0, -178849, -29127301]\) | \(632678989847546725777/80515134\) | \(80515134\) | \([2]\) | \(3840\) | \(1.3770\) | |
966.j2 | 966i4 | \([1, 0, 0, -12789, -316305]\) | \(231331938231569617/90942310746882\) | \(90942310746882\) | \([2]\) | \(3840\) | \(1.3770\) | |
966.j3 | 966i2 | \([1, 0, 0, -11179, -455731]\) | \(154502321244119857/55101928644\) | \(55101928644\) | \([2, 2]\) | \(1920\) | \(1.0304\) | |
966.j4 | 966i1 | \([1, 0, 0, -599, -9255]\) | \(-23771111713777/22848457968\) | \(-22848457968\) | \([4]\) | \(960\) | \(0.68384\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 966.j have rank \(0\).
Complex multiplication
The elliptic curves in class 966.j do not have complex multiplication.Modular form 966.2.a.j
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.