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SageMath
sage: E = EllipticCurve("48400.l1")
sage: E.isogeny_class()
Elliptic curves in class 48400.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 48400.l1 | 48400cn3 | [0, 1, 0, -125033, -17055062] | [2] | 207360 | |
| 48400.l2 | 48400cn4 | [0, 1, 0, -109908, -21320312] | [2] | 414720 | |
| 48400.l3 | 48400cn1 | [0, 1, 0, -4033, 66438] | [2] | 69120 | \(\Gamma_0(N)\)-optimal |
| 48400.l4 | 48400cn2 | [0, 1, 0, 11092, 459688] | [2] | 138240 |
Rank
sage: E.rank()
The elliptic curves in class 48400.l have rank \(1\).
Modular form 48400.2.a.l
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.
