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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7800.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7800.a1 | 7800n3 | \([0, -1, 0, -14040008, -20244113988]\) | \(19129597231400697604/26325\) | \(421200000000\) | \([2]\) | \(147456\) | \(2.3968\) | |
| 7800.a2 | 7800n2 | \([0, -1, 0, -877508, -316088988]\) | \(18681746265374416/693005625\) | \(2772022500000000\) | \([2, 2]\) | \(73728\) | \(2.0502\) | |
| 7800.a3 | 7800n4 | \([0, -1, 0, -837008, -346625988]\) | \(-4053153720264484/903687890625\) | \(-14459006250000000000\) | \([2]\) | \(147456\) | \(2.3968\) | |
| 7800.a4 | 7800n1 | \([0, -1, 0, -57383, -4441488]\) | \(83587439220736/13990184325\) | \(3497546081250000\) | \([2]\) | \(36864\) | \(1.7037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7800.a have rank \(0\).
Complex multiplication
The elliptic curves in class 7800.a do not have complex multiplication.Modular form 7800.2.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.
