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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 60840bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60840.p4 | 60840bj1 | \([0, 0, 0, 256542, -3337243]\) | \(33165879296/19278675\) | \(-1085387478025546800\) | \([2]\) | \(516096\) | \(2.1502\) | \(\Gamma_0(N)\)-optimal |
| 60840.p3 | 60840bj2 | \([0, 0, 0, -1028703, -26728702]\) | \(133649126224/77000625\) | \(69362040015833760000\) | \([2, 2]\) | \(1032192\) | \(2.4967\) | |
| 60840.p2 | 60840bj3 | \([0, 0, 0, -10915203, 13828212398]\) | \(39914580075556/172718325\) | \(622337565188219212800\) | \([2]\) | \(2064384\) | \(2.8433\) | |
| 60840.p1 | 60840bj4 | \([0, 0, 0, -11706123, -15378723178]\) | \(49235161015876/137109375\) | \(494031624044400000000\) | \([2]\) | \(2064384\) | \(2.8433\) |
Rank
sage: E.rank()
The elliptic curves in class 60840bj have rank \(1\).
Complex multiplication
The elliptic curves in class 60840bj do not have complex multiplication.Modular form 60840.2.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.
