Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 64400.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.m1 | 64400ca4 | \([0, 1, 0, -66732408, 209800175188]\) | \(513516182162686336369/1944885031250\) | \(124472642000000000000\) | \([2]\) | \(8626176\) | \(3.0705\) | |
| 64400.m2 | 64400ca3 | \([0, 1, 0, -4232408, 3175175188]\) | \(131010595463836369/7704101562500\) | \(493062500000000000000\) | \([2]\) | \(4313088\) | \(2.7239\) | |
| 64400.m3 | 64400ca2 | \([0, 1, 0, -1136408, 49559188]\) | \(2535986675931409/1450751712200\) | \(92848109580800000000\) | \([2]\) | \(2875392\) | \(2.5212\) | |
| 64400.m4 | 64400ca1 | \([0, 1, 0, -736408, -242440812]\) | \(690080604747409/3406760000\) | \(218032640000000000\) | \([2]\) | \(1437696\) | \(2.1746\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.m have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.m do not have complex multiplication.Modular form 64400.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
