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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 48960cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48960.d4 | 48960cj1 | \([0, 0, 0, -728508, -7265118832]\) | \(-3579968623693264/1906997690433375\) | \(-22777058366684043264000\) | \([2]\) | \(3440640\) | \(2.9691\) | \(\Gamma_0(N)\)-optimal |
| 48960.d3 | 48960cj2 | \([0, 0, 0, -60863628, -180863183248]\) | \(521902963282042184836/6241849278890625\) | \(298208993234863104000000\) | \([2, 2]\) | \(6881280\) | \(3.3157\) | |
| 48960.d2 | 48960cj3 | \([0, 0, 0, -112883628, 174100488752]\) | \(1664865424893526702418/826424127435466125\) | \(78966055095560412217344000\) | \([2]\) | \(13762560\) | \(3.6622\) | |
| 48960.d1 | 48960cj4 | \([0, 0, 0, -971005548, -11646102977872]\) | \(1059623036730633329075378/154307373046875\) | \(14744299104000000000000\) | \([2]\) | \(13762560\) | \(3.6622\) |
Rank
sage: E.rank()
The elliptic curves in class 48960cj have rank \(1\).
Complex multiplication
The elliptic curves in class 48960cj do not have complex multiplication.Modular form 48960.2.a.cj
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.
