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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 53130a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.c2 | 53130a1 | \([1, 1, 0, -1899828, 1007172432]\) | \(-758345163989747524609609/51164280992563200\) | \(-51164280992563200\) | \([2]\) | \(1148928\) | \(2.2612\) | \(\Gamma_0(N)\)-optimal |
53130.c1 | 53130a2 | \([1, 1, 0, -30397748, 64494838608]\) | \(3106332678537492823015958089/14138530560000\) | \(14138530560000\) | \([2]\) | \(2297856\) | \(2.6077\) |
Rank
sage: E.rank()
The elliptic curves in class 53130a have rank \(1\).
Complex multiplication
The elliptic curves in class 53130a do not have complex multiplication.Modular form 53130.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.