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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 62400a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.cp3 | 62400a1 | \([0, -1, 0, -6508, 204262]\) | \(30488290624/195\) | \(195000000\) | \([2]\) | \(36864\) | \(0.77535\) | \(\Gamma_0(N)\)-optimal |
| 62400.cp2 | 62400a2 | \([0, -1, 0, -6633, 196137]\) | \(504358336/38025\) | \(2433600000000\) | \([2, 2]\) | \(73728\) | \(1.1219\) | |
| 62400.cp4 | 62400a3 | \([0, -1, 0, 6367, 859137]\) | \(55742968/658125\) | \(-336960000000000\) | \([2]\) | \(147456\) | \(1.4685\) | |
| 62400.cp1 | 62400a4 | \([0, -1, 0, -21633, -988863]\) | \(2186875592/428415\) | \(219348480000000\) | \([2]\) | \(147456\) | \(1.4685\) |
Rank
sage: E.rank()
The elliptic curves in class 62400a have rank \(1\).
Complex multiplication
The elliptic curves in class 62400a do not have complex multiplication.Modular form 62400.2.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 Cremona 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 Cremona labels.
