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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 161700.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.bq1 | 161700en2 | \([0, -1, 0, -45870533, -119562024063]\) | \(462893166690304/4125\) | \(95119216500000000\) | \([]\) | \(7838208\) | \(2.8410\) | |
161700.bq2 | 161700en1 | \([0, -1, 0, -594533, -146574063]\) | \(1007878144/179685\) | \(4143393070740000000\) | \([]\) | \(2612736\) | \(2.2917\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 161700.bq do not have complex multiplication.Modular form 161700.2.a.bq
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.