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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 70805.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70805.be1 | 70805f2 | \([0, 1, 1, -2446481, 864592306]\) | \(1369177719046144/518798828125\) | \(613604583038330078125\) | \([]\) | \(2384640\) | \(2.6883\) | |
70805.be2 | 70805f1 | \([0, 1, 1, -1070841, -426824135]\) | \(114817869021184/15353125\) | \(18158768588603125\) | \([]\) | \(794880\) | \(2.1390\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 70805.be have rank \(0\).
Complex multiplication
The elliptic curves in class 70805.be do not have complex multiplication.Modular form 70805.2.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.