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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 18240.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18240.cc1 | 18240ci4 | \([0, 1, 0, -3380700481, 75657448009919]\) | \(16300610738133468173382620881/2228489100\) | \(584185046630400\) | \([2]\) | \(4608000\) | \(3.6485\) | |
18240.cc2 | 18240ci3 | \([0, 1, 0, -211293761, 1182095022015]\) | \(-3979640234041473454886161/1471455901872240\) | \(-385733335940396482560\) | \([2]\) | \(2304000\) | \(3.3020\) | |
18240.cc3 | 18240ci2 | \([0, 1, 0, -5628481, 4426230719]\) | \(75224183150104868881/11219310000000000\) | \(2941074800640000000000\) | \([2]\) | \(921600\) | \(2.8438\) | |
18240.cc4 | 18240ci1 | \([0, 1, 0, 597439, 378137535]\) | \(89962967236397039/287450726400000\) | \(-75353483221401600000\) | \([2]\) | \(460800\) | \(2.4973\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 18240.cc do not have complex multiplication.Modular form 18240.2.a.cc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.