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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 14784.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14784.p1 | 14784r4 | \([0, -1, 0, -904513, -330783935]\) | \(312196988566716625/25367712678\) | \(6649993672261632\) | \([2]\) | \(110592\) | \(2.0813\) | |
| 14784.p2 | 14784r3 | \([0, -1, 0, -52673, -5892159]\) | \(-61653281712625/21875235228\) | \(-5734461663608832\) | \([2]\) | \(55296\) | \(1.7347\) | |
| 14784.p3 | 14784r2 | \([0, -1, 0, -23233, 691393]\) | \(5290763640625/2291573592\) | \(600722267701248\) | \([2]\) | \(36864\) | \(1.5320\) | |
| 14784.p4 | 14784r1 | \([0, -1, 0, 4927, 77505]\) | \(50447927375/39517632\) | \(-10359310123008\) | \([2]\) | \(18432\) | \(1.1854\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.p have rank \(1\).
Complex multiplication
The elliptic curves in class 14784.p do not have complex multiplication.Modular form 14784.2.a.p
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.
