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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 121680.fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121680.fo1 | 121680bv4 | \([0, 0, 0, -12655227, 17328182794]\) | \(31103978031362/195\) | \(1405245508392960\) | \([4]\) | \(4128768\) | \(2.5122\) | |
| 121680.fo2 | 121680bv3 | \([0, 0, 0, -1095627, 43417114]\) | \(20183398562/11567205\) | \(83357758312361994240\) | \([2]\) | \(4128768\) | \(2.5122\) | |
| 121680.fo3 | 121680bv2 | \([0, 0, 0, -791427, 270411154]\) | \(15214885924/38025\) | \(137011437068313600\) | \([2, 2]\) | \(2064384\) | \(2.1656\) | |
| 121680.fo4 | 121680bv1 | \([0, 0, 0, -30927, 7430254]\) | \(-3631696/24375\) | \(-21956961068640000\) | \([2]\) | \(1032192\) | \(1.8190\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121680.fo have rank \(1\).
Complex multiplication
The elliptic curves in class 121680.fo do not have complex multiplication.Modular form 121680.2.a.fo
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
