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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 13200.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.a1 | 13200bn3 | \([0, -1, 0, -641008, -197319488]\) | \(455129268177961/4392300\) | \(281107200000000\) | \([2]\) | \(147456\) | \(1.9339\) | |
| 13200.a2 | 13200bn2 | \([0, -1, 0, -41008, -2919488]\) | \(119168121961/10890000\) | \(696960000000000\) | \([2, 2]\) | \(73728\) | \(1.5873\) | |
| 13200.a3 | 13200bn1 | \([0, -1, 0, -9008, 280512]\) | \(1263214441/211200\) | \(13516800000000\) | \([2]\) | \(36864\) | \(1.2407\) | \(\Gamma_0(N)\)-optimal |
| 13200.a4 | 13200bn4 | \([0, -1, 0, 46992, -13831488]\) | \(179310732119/1392187500\) | \(-89100000000000000\) | \([2]\) | \(147456\) | \(1.9339\) |
Rank
sage: E.rank()
The elliptic curves in class 13200.a have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.a do not have complex multiplication.Modular form 13200.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
