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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 397800.dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.dh1 | 397800dh1 | \([0, 0, 0, -82575, -9132750]\) | \(21354132816/1105\) | \(3222180000000\) | \([2]\) | \(1179648\) | \(1.4692\) | \(\Gamma_0(N)\)-optimal |
397800.dh2 | 397800dh2 | \([0, 0, 0, -78075, -10172250]\) | \(-4512447684/1221025\) | \(-14242035600000000\) | \([2]\) | \(2359296\) | \(1.8158\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.dh have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.dh do not have complex multiplication.Modular form 397800.2.a.dh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.