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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 304704cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304704.cb2 | 304704cb1 | \([0, 0, 0, 146004, 1338759344]\) | \(4/9\) | \(-774462676130774581248\) | \([2]\) | \(13565952\) | \(2.6872\) | \(\Gamma_0(N)\)-optimal |
304704.cb1 | 304704cb2 | \([0, 0, 0, -17374476, 27290094320]\) | \(3370318/81\) | \(13940328170353942462464\) | \([2]\) | \(27131904\) | \(3.0338\) |
Rank
sage: E.rank()
The elliptic curves in class 304704cb have rank \(1\).
Complex multiplication
The elliptic curves in class 304704cb do not have complex multiplication.Modular form 304704.2.a.cb
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.