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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 4560.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.bb1 | 4560g3 | \([0, 1, 0, -30400, -2050300]\) | \(3034301922374404/1425\) | \(1459200\) | \([2]\) | \(4096\) | \(0.95645\) | |
| 4560.bb2 | 4560g4 | \([0, 1, 0, -2280, -18972]\) | \(1280615525284/601171875\) | \(615600000000\) | \([4]\) | \(4096\) | \(0.95645\) | |
| 4560.bb3 | 4560g2 | \([0, 1, 0, -1900, -32500]\) | \(2964647793616/2030625\) | \(519840000\) | \([2, 2]\) | \(2048\) | \(0.60988\) | |
| 4560.bb4 | 4560g1 | \([0, 1, 0, -95, -732]\) | \(-5988775936/9774075\) | \(-156385200\) | \([2]\) | \(1024\) | \(0.26330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 4560.bb do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
