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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 40560z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.cs4 | 40560z1 | \([0, 1, 0, 14140, -452100]\) | \(253012016/219375\) | \(-271073593440000\) | \([2]\) | \(129024\) | \(1.4570\) | \(\Gamma_0(N)\)-optimal |
| 40560.cs3 | 40560z2 | \([0, 1, 0, -70360, -4068700]\) | \(7793764996/3080025\) | \(15223493007590400\) | \([2, 2]\) | \(258048\) | \(1.8036\) | |
| 40560.cs2 | 40560z3 | \([0, 1, 0, -509760, 137066580]\) | \(1481943889298/34543665\) | \(341474658539489280\) | \([4]\) | \(516096\) | \(2.1501\) | |
| 40560.cs1 | 40560z4 | \([0, 1, 0, -982960, -375314380]\) | \(10625310339698/3855735\) | \(38115115826411520\) | \([2]\) | \(516096\) | \(2.1501\) |
Rank
sage: E.rank()
The elliptic curves in class 40560z have rank \(1\).
Complex multiplication
The elliptic curves in class 40560z do not have complex multiplication.Modular form 40560.2.a.z
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.
