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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 364650.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.b1 | 364650b4 | \([1, 1, 0, -290425831625, -60242342153812875]\) | \(173384156893208913680898166749513361/466915159846072080\) | \(7295549372594876250000\) | \([2]\) | \(1528823808\) | \(4.7974\) | |
364650.b2 | 364650b2 | \([1, 1, 0, -18151621625, -941291490022875]\) | \(42330166443562126960455979919761/69464630166853628678400\) | \(1085384846357087948100000000\) | \([2, 2]\) | \(764411904\) | \(4.4508\) | |
364650.b3 | 364650b3 | \([1, 1, 0, -17975203625, -960484533496875]\) | \(-41107885916860358643135963073681/1716440731291073126286090000\) | \(-26819386426423017598220156250000\) | \([2]\) | \(1528823808\) | \(4.7974\) | |
364650.b4 | 364650b1 | \([1, 1, 0, -1145509625, -14407367686875]\) | \(10638978093366640576603658641/418238874164098875064320\) | \(6534982408814044922880000000\) | \([2]\) | \(382205952\) | \(4.1043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.b have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.b do not have complex multiplication.Modular form 364650.2.a.b
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.