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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 299538.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299538.a1 | 299538a2 | \([1, -1, 0, -102966, 13912136]\) | \(-35937/4\) | \(-13437726000494436\) | \([]\) | \(2830464\) | \(1.8321\) | |
299538.a2 | 299538a1 | \([1, -1, 0, 7974, -29324]\) | \(109503/64\) | \(-32769946046016\) | \([]\) | \(943488\) | \(1.2828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 299538.a have rank \(0\).
Complex multiplication
The elliptic curves in class 299538.a do not have complex multiplication.Modular form 299538.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.