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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 112710.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.be1 | 112710bg1 | \([1, 0, 1, -23849, 2249696]\) | \(-215038729/189540\) | \(-1322185065367140\) | \([3]\) | \(528768\) | \(1.5987\) | \(\Gamma_0(N)\)-optimal |
112710.be2 | 112710bg2 | \([1, 0, 1, 197236, -37634038]\) | \(121644944711/158184000\) | \(-1103453215047144000\) | \([]\) | \(1586304\) | \(2.1480\) |
Rank
sage: E.rank()
The elliptic curves in class 112710.be have rank \(0\).
Complex multiplication
The elliptic curves in class 112710.be do not have complex multiplication.Modular form 112710.2.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.