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SageMath
E = EllipticCurve("baw1")
E.isogeny_class()
Elliptic curves in class 235200baw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.baw3 | 235200baw1 | \([0, 1, 0, -24908, 1503438]\) | \(14526784/15\) | \(1764735000000\) | \([2]\) | \(589824\) | \(1.2678\) | \(\Gamma_0(N)\)-optimal |
235200.baw2 | 235200baw2 | \([0, 1, 0, -31033, 701063]\) | \(438976/225\) | \(1694145600000000\) | \([2, 2]\) | \(1179648\) | \(1.6144\) | |
235200.baw4 | 235200baw3 | \([0, 1, 0, 115967, 5552063]\) | \(2863288/1875\) | \(-112943040000000000\) | \([2]\) | \(2359296\) | \(1.9610\) | |
235200.baw1 | 235200baw4 | \([0, 1, 0, -276033, -55403937]\) | \(38614472/405\) | \(24395696640000000\) | \([2]\) | \(2359296\) | \(1.9610\) |
Rank
sage: E.rank()
The elliptic curves in class 235200baw have rank \(0\).
Complex multiplication
The elliptic curves in class 235200baw do not have complex multiplication.Modular form 235200.2.a.baw
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.