Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 18480w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.ce4 | 18480w1 | \([0, 1, 0, 364, -2436]\) | \(20777545136/23059575\) | \(-5903251200\) | \([2]\) | \(8192\) | \(0.56140\) | \(\Gamma_0(N)\)-optimal |
| 18480.ce3 | 18480w2 | \([0, 1, 0, -2056, -24700]\) | \(939083699236/300155625\) | \(307359360000\) | \([2, 2]\) | \(16384\) | \(0.90798\) | |
| 18480.ce1 | 18480w3 | \([0, 1, 0, -29776, -1987276]\) | \(1425631925916578/270703125\) | \(554400000000\) | \([2]\) | \(32768\) | \(1.2545\) | |
| 18480.ce2 | 18480w4 | \([0, 1, 0, -13056, 551700]\) | \(120186986927618/4332064275\) | \(8872067635200\) | \([4]\) | \(32768\) | \(1.2545\) |
Rank
sage: E.rank()
The elliptic curves in class 18480w have rank \(1\).
Complex multiplication
The elliptic curves in class 18480w do not have complex multiplication.Modular form 18480.2.a.w
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.
