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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 11970.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11970.m1 | 11970e3 | \([1, -1, 0, -162960, -25225984]\) | \(24315150763476243/59584000000\) | \(1172791872000000\) | \([2]\) | \(82944\) | \(1.7697\) | |
| 11970.m2 | 11970e4 | \([1, -1, 0, -102480, -44228800]\) | \(-6047169663613203/39484375000000\) | \(-777170953125000000\) | \([2]\) | \(165888\) | \(2.1163\) | |
| 11970.m3 | 11970e1 | \([1, -1, 0, -9345, 319725]\) | \(3342904779518667/322781796400\) | \(8715108502800\) | \([6]\) | \(27648\) | \(1.2204\) | \(\Gamma_0(N)\)-optimal |
| 11970.m4 | 11970e2 | \([1, -1, 0, 11235, 1517481]\) | \(5808412272111093/40341842957500\) | \(-1089229759852500\) | \([6]\) | \(55296\) | \(1.5670\) |
Rank
sage: E.rank()
The elliptic curves in class 11970.m have rank \(1\).
Complex multiplication
The elliptic curves in class 11970.m do not have complex multiplication.Modular form 11970.2.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.
