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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 96600.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.bj1 | 96600br4 | \([0, -1, 0, -973008, -367103988]\) | \(3183636045638162/19833730875\) | \(634679388000000000\) | \([2]\) | \(2359296\) | \(2.2538\) | |
| 96600.bj2 | 96600br2 | \([0, -1, 0, -98008, 2146012]\) | \(6507178816324/3645140625\) | \(58322250000000000\) | \([2, 2]\) | \(1179648\) | \(1.9073\) | |
| 96600.bj3 | 96600br1 | \([0, -1, 0, -73508, 7683012]\) | \(10981797946576/20708625\) | \(82834500000000\) | \([4]\) | \(589824\) | \(1.5607\) | \(\Gamma_0(N)\)-optimal |
| 96600.bj4 | 96600br3 | \([0, -1, 0, 384992, 16636012]\) | \(197209449637198/117919921875\) | \(-3773437500000000000\) | \([2]\) | \(2359296\) | \(2.2538\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.bj do not have complex multiplication.Modular form 96600.2.a.bj
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.
