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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 510.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
510.a1 | 510a2 | \([1, 1, 0, -46193, 3801813]\) | \(10901014250685308569/1040774054400\) | \(1040774054400\) | \([2]\) | \(2016\) | \(1.3426\) | |
510.a2 | 510a1 | \([1, 1, 0, -2673, 67797]\) | \(-2113364608155289/828431400960\) | \(-828431400960\) | \([2]\) | \(1008\) | \(0.99603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 510.a have rank \(0\).
Complex multiplication
The elliptic curves in class 510.a do not have complex multiplication.Modular form 510.2.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.