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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 206400du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.n3 | 206400du1 | \([0, -1, 0, -7633, 137137]\) | \(192143824/80625\) | \(20640000000000\) | \([2]\) | \(589824\) | \(1.2518\) | \(\Gamma_0(N)\)-optimal |
| 206400.n2 | 206400du2 | \([0, -1, 0, -57633, -5212863]\) | \(20674973956/416025\) | \(426009600000000\) | \([2, 2]\) | \(1179648\) | \(1.5984\) | |
| 206400.n4 | 206400du3 | \([0, -1, 0, 2367, -15592863]\) | \(715822/51282015\) | \(-105025566720000000\) | \([4]\) | \(2359296\) | \(1.9450\) | |
| 206400.n1 | 206400du4 | \([0, -1, 0, -917633, -338032863]\) | \(41725476313778/17415\) | \(35665920000000\) | \([2]\) | \(2359296\) | \(1.9450\) |
Rank
sage: E.rank()
The elliptic curves in class 206400du have rank \(1\).
Complex multiplication
The elliptic curves in class 206400du do not have complex multiplication.Modular form 206400.2.a.du
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.
