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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100016b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100016.k3 | 100016b1 | \([0, 0, 0, -314, 2123]\) | \(213989603328/2144093\) | \(34305488\) | \([2]\) | \(21248\) | \(0.26428\) | \(\Gamma_0(N)\)-optimal |
| 100016.k2 | 100016b2 | \([0, 0, 0, -559, -1650]\) | \(75460411728/39075001\) | \(10003200256\) | \([2, 2]\) | \(42496\) | \(0.61085\) | |
| 100016.k4 | 100016b3 | \([0, 0, 0, 2101, -12822]\) | \(1001617520508/648997573\) | \(-664573514752\) | \([2]\) | \(84992\) | \(0.95743\) | |
| 100016.k1 | 100016b4 | \([0, 0, 0, -7139, -231950]\) | \(39294874074852/42875609\) | \(43904623616\) | \([2]\) | \(84992\) | \(0.95743\) |
Rank
sage: E.rank()
The elliptic curves in class 100016b have rank \(0\).
Complex multiplication
The elliptic curves in class 100016b do not have complex multiplication.Modular form 100016.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
