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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 244398bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244398.bj4 | 244398bj1 | \([1, 0, 0, -51324, -16369920]\) | \(-100999381393/723148272\) | \(-107051897324333808\) | \([2]\) | \(2433024\) | \(1.9508\) | \(\Gamma_0(N)\)-optimal |
| 244398.bj3 | 244398bj2 | \([1, 0, 0, -1331504, -590146596]\) | \(1763535241378513/4612311396\) | \(682787617851691044\) | \([2, 2]\) | \(4866048\) | \(2.2974\) | |
| 244398.bj2 | 244398bj3 | \([1, 0, 0, -1855214, -82881090]\) | \(4770223741048753/2740574865798\) | \(405703436629462624422\) | \([2]\) | \(9732096\) | \(2.6440\) | |
| 244398.bj1 | 244398bj4 | \([1, 0, 0, -21290674, -37813998646]\) | \(7209828390823479793/49509306\) | \(7329154127483034\) | \([2]\) | \(9732096\) | \(2.6440\) |
Rank
sage: E.rank()
The elliptic curves in class 244398bj have rank \(1\).
Complex multiplication
The elliptic curves in class 244398bj do not have complex multiplication.Modular form 244398.2.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 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.
