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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 32674b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32674.a2 | 32674b1 | \([1, -1, 1, 300, -1053001]\) | \(3375/539648\) | \(-478939586444288\) | \([2]\) | \(153600\) | \(1.4958\) | \(\Gamma_0(N)\)-optimal |
32674.a1 | 32674b2 | \([1, -1, 1, -153460, -22702409]\) | \(450335804625/8887328\) | \(7887536314254368\) | \([2]\) | \(307200\) | \(1.8423\) |
Rank
sage: E.rank()
The elliptic curves in class 32674b have rank \(0\).
Complex multiplication
The elliptic curves in class 32674b do not have complex multiplication.Modular form 32674.2.a.b
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.