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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4010.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4010.a1 | 4010c1 | \([1, 0, 1, -39508, 3019218]\) | \(-6819665063040893881/802000000\) | \(-802000000\) | \([3]\) | \(11984\) | \(1.1301\) | \(\Gamma_0(N)\)-optimal |
4010.a2 | 4010c2 | \([1, 0, 1, -34883, 3753918]\) | \(-4694045543427107881/3380671990988800\) | \(-3380671990988800\) | \([]\) | \(35952\) | \(1.6795\) |
Rank
sage: E.rank()
The elliptic curves in class 4010.a have rank \(0\).
Complex multiplication
The elliptic curves in class 4010.a do not have complex multiplication.Modular form 4010.2.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.