Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 360d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360.e4 | 360d1 | \([0, 0, 0, 33, 34]\) | \(21296/15\) | \(-2799360\) | \([4]\) | \(64\) | \(-0.074438\) | \(\Gamma_0(N)\)-optimal |
| 360.e3 | 360d2 | \([0, 0, 0, -147, 286]\) | \(470596/225\) | \(167961600\) | \([2, 2]\) | \(128\) | \(0.27214\) | |
| 360.e2 | 360d3 | \([0, 0, 0, -1227, -16346]\) | \(136835858/1875\) | \(2799360000\) | \([2]\) | \(256\) | \(0.61871\) | |
| 360.e1 | 360d4 | \([0, 0, 0, -1947, 33046]\) | \(546718898/405\) | \(604661760\) | \([2]\) | \(256\) | \(0.61871\) |
Rank
sage: E.rank()
The elliptic curves in class 360d have rank \(0\).
Complex multiplication
The elliptic curves in class 360d do not have complex multiplication.Modular form 360.2.a.d
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.
