Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 117600m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.cd3 | 117600m1 | \([0, -1, 0, -203758, -23967488]\) | \(7952095936/2480625\) | \(291843050625000000\) | \([2, 2]\) | \(1179648\) | \(2.0556\) | \(\Gamma_0(N)\)-optimal |
| 117600.cd4 | 117600m2 | \([0, -1, 0, 567992, -162882488]\) | \(21531355768/24609375\) | \(-23162146875000000000\) | \([2]\) | \(2359296\) | \(2.4021\) | |
| 117600.cd2 | 117600m3 | \([0, -1, 0, -1275633, 536623137]\) | \(30488290624/1148175\) | \(8645224996800000000\) | \([2]\) | \(2359296\) | \(2.4021\) | |
| 117600.cd1 | 117600m4 | \([0, -1, 0, -2960008, -1958854988]\) | \(3047363673992/540225\) | \(508455448200000000\) | \([2]\) | \(2359296\) | \(2.4021\) |
Rank
sage: E.rank()
The elliptic curves in class 117600m have rank \(0\).
Complex multiplication
The elliptic curves in class 117600m do not have complex multiplication.Modular form 117600.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
