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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 250173.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250173.be1 | 250173be2 | \([0, 0, 1, -6900876, 6977562959]\) | \(39248538107904/71687\) | \(66382454176354701\) | \([]\) | \(5598720\) | \(2.4848\) | |
250173.be2 | 250173be1 | \([0, 0, 1, -110466, 3434644]\) | \(117361115136/63905303\) | \(81174994565587461\) | \([]\) | \(1866240\) | \(1.9355\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250173.be have rank \(0\).
Complex multiplication
The elliptic curves in class 250173.be do not have complex multiplication.Modular form 250173.2.a.be
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.