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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 151620a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151620.q1 | 151620a1 | \([0, 1, 0, -204085, -35553700]\) | \(1248870793216/42525\) | \(32010017432400\) | \([2]\) | \(855360\) | \(1.6831\) | \(\Gamma_0(N)\)-optimal |
151620.q2 | 151620a2 | \([0, 1, 0, -195060, -38831580]\) | \(-68150496976/14467005\) | \(-174236926888039680\) | \([2]\) | \(1710720\) | \(2.0297\) |
Rank
sage: E.rank()
The elliptic curves in class 151620a have rank \(0\).
Complex multiplication
The elliptic curves in class 151620a do not have complex multiplication.Modular form 151620.2.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.