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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 182070db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.a4 | 182070db1 | \([1, -1, 0, 40637970, -33532924460]\) | \(421792317902132351/271682182840320\) | \(-4780597879662174346936320\) | \([2]\) | \(41287680\) | \(3.4245\) | \(\Gamma_0(N)\)-optimal |
182070.a3 | 182070db2 | \([1, -1, 0, -172435950, -275627512364]\) | \(32224493437735955329/16782725759385600\) | \(295313672547405294535065600\) | \([2, 2]\) | \(82575360\) | \(3.7710\) | |
182070.a2 | 182070db3 | \([1, -1, 0, -1559081070, 23494520463700]\) | \(23818189767728437646209/232359312482640000\) | \(4088661335687025256274640000\) | \([2]\) | \(165150720\) | \(4.1176\) | |
182070.a1 | 182070db4 | \([1, -1, 0, -2194973550, -39542386001324]\) | \(66464620505913166201729/74880071980801920\) | \(1317611297133786731093377920\) | \([2]\) | \(165150720\) | \(4.1176\) |
Rank
sage: E.rank()
The elliptic curves in class 182070db have rank \(0\).
Complex multiplication
The elliptic curves in class 182070db do not have complex multiplication.Modular form 182070.2.a.db
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 Cremona 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 Cremona labels.