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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 115920.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.dk1 | 115920ek1 | \([0, 0, 0, -16169187, 25025360866]\) | \(156567200830221067489/16905000000\) | \(50478059520000000\) | \([2]\) | \(3354624\) | \(2.6319\) | \(\Gamma_0(N)\)-optimal |
115920.dk2 | 115920ek2 | \([0, 0, 0, -16128867, 25156376674]\) | \(-155398856216042825569/1627294921875000\) | \(-4859076600000000000000\) | \([2]\) | \(6709248\) | \(2.9785\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.dk have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.dk do not have complex multiplication.Modular form 115920.2.a.dk
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.