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SageMath
E = EllipticCurve("bbi1")
E.isogeny_class()
Elliptic curves in class 235200.bbi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.bbi1 | 235200bbi4 | \([0, 1, 0, -29284033, -61004739937]\) | \(5763259856089/5670\) | \(2732318023680000000\) | \([2]\) | \(14155776\) | \(2.8310\) | |
| 235200.bbi2 | 235200bbi2 | \([0, 1, 0, -1844033, -938579937]\) | \(1439069689/44100\) | \(21251362406400000000\) | \([2, 2]\) | \(7077888\) | \(2.4844\) | |
| 235200.bbi3 | 235200bbi1 | \([0, 1, 0, -276033, 35148063]\) | \(4826809/1680\) | \(809575710720000000\) | \([2]\) | \(3538944\) | \(2.1378\) | \(\Gamma_0(N)\)-optimal |
| 235200.bbi4 | 235200bbi3 | \([0, 1, 0, 507967, -3165923937]\) | \(30080231/9003750\) | \(-4338819824640000000000\) | \([2]\) | \(14155776\) | \(2.8310\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.bbi have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.bbi do not have complex multiplication.Modular form 235200.2.a.bbi
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.
