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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 106470.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106470.l1 | 106470a3 | \([1, -1, 0, -159990, -24560704]\) | \(4767078987/6860\) | \(651741719412420\) | \([2]\) | \(663552\) | \(1.7450\) | |
| 106470.l2 | 106470a4 | \([1, -1, 0, -114360, -38897650]\) | \(-1740992427/5882450\) | \(-558868524396150150\) | \([2]\) | \(1327104\) | \(2.0916\) | |
| 106470.l3 | 106470a1 | \([1, -1, 0, -7890, 238356]\) | \(416832723/56000\) | \(7298135208000\) | \([2]\) | \(221184\) | \(1.1957\) | \(\Gamma_0(N)\)-optimal |
| 106470.l4 | 106470a2 | \([1, -1, 0, 12390, 1248300]\) | \(1613964717/6125000\) | \(-798233538375000\) | \([2]\) | \(442368\) | \(1.5423\) |
Rank
sage: E.rank()
The elliptic curves in class 106470.l have rank \(1\).
Complex multiplication
The elliptic curves in class 106470.l do not have complex multiplication.Modular form 106470.2.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.
