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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 44352bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.cy4 | 44352bt1 | \([0, 0, 0, 44340, -2136976]\) | \(50447927375/39517632\) | \(-7551937079672832\) | \([2]\) | \(147456\) | \(1.7347\) | \(\Gamma_0(N)\)-optimal |
| 44352.cy3 | 44352bt2 | \([0, 0, 0, -209100, -18458512]\) | \(5290763640625/2291573592\) | \(437926533154209792\) | \([2]\) | \(294912\) | \(2.0813\) | |
| 44352.cy2 | 44352bt3 | \([0, 0, 0, -474060, 159562352]\) | \(-61653281712625/21875235228\) | \(-4180422552770838528\) | \([2]\) | \(442368\) | \(2.2840\) | |
| 44352.cy1 | 44352bt4 | \([0, 0, 0, -8140620, 8939306864]\) | \(312196988566716625/25367712678\) | \(4847845387078729728\) | \([2]\) | \(884736\) | \(2.6306\) |
Rank
sage: E.rank()
The elliptic curves in class 44352bt have rank \(1\).
Complex multiplication
The elliptic curves in class 44352bt do not have complex multiplication.Modular form 44352.2.a.bt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
