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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 428910.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
428910.w1 | 428910w4 | \([1, 0, 1, -5500999, -4966434334]\) | \(30949975477232209/478125000\) | \(284399900353125000\) | \([2]\) | \(19267584\) | \(2.4842\) | |
428910.w2 | 428910w2 | \([1, 0, 1, -354079, -72742798]\) | \(8253429989329/936360000\) | \(556968764851560000\) | \([2, 2]\) | \(9633792\) | \(2.1376\) | |
428910.w3 | 428910w1 | \([1, 0, 1, -84959, 8316146]\) | \(114013572049/15667200\) | \(9319215934771200\) | \([2]\) | \(4816896\) | \(1.7910\) | \(\Gamma_0(N)\)-optimal* |
428910.w4 | 428910w3 | \([1, 0, 1, 486921, -365747198]\) | \(21464092074671/109596256200\) | \(-65190409082050840200\) | \([2]\) | \(19267584\) | \(2.4842\) |
Rank
sage: E.rank()
The elliptic curves in class 428910.w have rank \(0\).
Complex multiplication
The elliptic curves in class 428910.w do not have complex multiplication.Modular form 428910.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.