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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1012.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1012.a1 | 1012d2 | \([0, 0, 0, -119, -498]\) | \(727988688/2783\) | \(712448\) | \([2]\) | \(132\) | \(-0.018317\) | |
1012.a2 | 1012d1 | \([0, 0, 0, -4, -15]\) | \(-442368/5819\) | \(-93104\) | \([2]\) | \(66\) | \(-0.36489\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1012.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1012.a do not have complex multiplication.Modular form 1012.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.