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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 20160t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.er2 | 20160t1 | \([0, 0, 0, -6732, 212336]\) | \(4767078987/6860\) | \(48554311680\) | \([2]\) | \(18432\) | \(0.95293\) | \(\Gamma_0(N)\)-optimal |
20160.er3 | 20160t2 | \([0, 0, 0, -4812, 335984]\) | \(-1740992427/5882450\) | \(-41635322265600\) | \([2]\) | \(36864\) | \(1.2995\) | |
20160.er1 | 20160t3 | \([0, 0, 0, -26892, -1487376]\) | \(416832723/56000\) | \(288947699712000\) | \([2]\) | \(55296\) | \(1.5022\) | |
20160.er4 | 20160t4 | \([0, 0, 0, 42228, -7874064]\) | \(1613964717/6125000\) | \(-31603654656000000\) | \([2]\) | \(110592\) | \(1.8488\) |
Rank
sage: E.rank()
The elliptic curves in class 20160t have rank \(1\).
Complex multiplication
The elliptic curves in class 20160t do not have complex multiplication.Modular form 20160.2.a.t
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 Cremona 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 Cremona labels.