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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 27930.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27930.db1 | 27930cw4 | \([1, 0, 0, -24131521, -45629351755]\) | \(13209596798923694545921/92340\) | \(10863708660\) | \([2]\) | \(1105920\) | \(2.4604\) | |
27930.db2 | 27930cw3 | \([1, 0, 0, -1526841, -694547379]\) | \(3345930611358906241/165622259047500\) | \(19485293154679327500\) | \([2]\) | \(1105920\) | \(2.4604\) | |
27930.db3 | 27930cw2 | \([1, 0, 0, -1508221, -713051935]\) | \(3225005357698077121/8526675600\) | \(1003154857664400\) | \([2, 2]\) | \(552960\) | \(2.1139\) | |
27930.db4 | 27930cw1 | \([1, 0, 0, -93101, -11435439]\) | \(-758575480593601/40535043840\) | \(-4768907372732160\) | \([2]\) | \(276480\) | \(1.7673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27930.db have rank \(0\).
Complex multiplication
The elliptic curves in class 27930.db do not have complex multiplication.Modular form 27930.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.