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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 16720.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16720.u1 | 16720bh3 | \([0, 0, 0, -16268627, 22217544146]\) | \(116256292809537371612841/15216540068579856875\) | \(62326948120903093760000\) | \([2]\) | \(1130496\) | \(3.1021\) | |
| 16720.u2 | 16720bh2 | \([0, 0, 0, -15718627, 23986234146]\) | \(104859453317683374662841/2223652969140625\) | \(9108082561600000000\) | \([2, 2]\) | \(565248\) | \(2.7555\) | |
| 16720.u3 | 16720bh1 | \([0, 0, 0, -15718547, 23986490514]\) | \(104857852278310619039721/47155625\) | \(193149440000\) | \([2]\) | \(282624\) | \(2.4090\) | \(\Gamma_0(N)\)-optimal |
| 16720.u4 | 16720bh4 | \([0, 0, 0, -15169907, 25738516594]\) | \(-94256762600623910012361/15323275604248046875\) | \(-62764136875000000000000\) | \([4]\) | \(1130496\) | \(3.1021\) |
Rank
sage: E.rank()
The elliptic curves in class 16720.u have rank \(0\).
Complex multiplication
The elliptic curves in class 16720.u do not have complex multiplication.Modular form 16720.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
