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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 55440.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.p1 | 55440bu3 | \([0, 0, 0, -9288, -27837]\) | \(281370820608/161767375\) | \(50945075874000\) | \([2]\) | \(124416\) | \(1.3198\) | |
| 55440.p2 | 55440bu1 | \([0, 0, 0, -6648, -208633]\) | \(75216478666752/326095\) | \(140873040\) | \([2]\) | \(41472\) | \(0.77046\) | \(\Gamma_0(N)\)-optimal |
| 55440.p3 | 55440bu2 | \([0, 0, 0, -6543, -215542]\) | \(-4481782160112/310023175\) | \(-2142880185600\) | \([2]\) | \(82944\) | \(1.1170\) | |
| 55440.p4 | 55440bu4 | \([0, 0, 0, 37017, -222318]\) | \(1113258734352/648484375\) | \(-3267614196000000\) | \([2]\) | \(248832\) | \(1.6663\) |
Rank
sage: E.rank()
The elliptic curves in class 55440.p have rank \(0\).
Complex multiplication
The elliptic curves in class 55440.p do not have complex multiplication.Modular form 55440.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
