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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 15288.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15288.bb1 | 15288j3 | \([0, 1, 0, -14912, 678768]\) | \(3044193988/85293\) | \(10275467424768\) | \([2]\) | \(36864\) | \(1.2758\) | |
| 15288.bb2 | 15288j2 | \([0, 1, 0, -2172, -24480]\) | \(37642192/13689\) | \(412287273216\) | \([2, 2]\) | \(18432\) | \(0.92921\) | |
| 15288.bb3 | 15288j1 | \([0, 1, 0, -1927, -33202]\) | \(420616192/117\) | \(220238928\) | \([2]\) | \(9216\) | \(0.58264\) | \(\Gamma_0(N)\)-optimal |
| 15288.bb4 | 15288j4 | \([0, 1, 0, 6648, -165600]\) | \(269676572/257049\) | \(-30967355188224\) | \([2]\) | \(36864\) | \(1.2758\) |
Rank
sage: E.rank()
The elliptic curves in class 15288.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 15288.bb do not have complex multiplication.Modular form 15288.2.a.bb
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.
