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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 288834bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288834.bx3 | 288834bx1 | \([1, 0, 0, -3714, 77748]\) | \(38272753/4368\) | \(646620763152\) | \([2]\) | \(608256\) | \(0.99857\) | \(\Gamma_0(N)\)-optimal |
| 288834.bx2 | 288834bx2 | \([1, 0, 0, -14294, -576096]\) | \(2181825073/298116\) | \(44131867085124\) | \([2, 2]\) | \(1216512\) | \(1.3451\) | |
| 288834.bx4 | 288834bx3 | \([1, 0, 0, 22736, -3057106]\) | \(8780064047/32388174\) | \(-4794612131176686\) | \([2]\) | \(2433024\) | \(1.6917\) | |
| 288834.bx1 | 288834bx4 | \([1, 0, 0, -220604, -39898782]\) | \(8020417344913/187278\) | \(27723865220142\) | \([2]\) | \(2433024\) | \(1.6917\) |
Rank
sage: E.rank()
The elliptic curves in class 288834bx have rank \(0\).
Complex multiplication
The elliptic curves in class 288834bx do not have complex multiplication.Modular form 288834.2.a.bx
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.
