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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 306d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
306.d1 | 306d1 | \([1, -1, 1, -23, -21]\) | \(1771561/612\) | \(446148\) | \([2]\) | \(64\) | \(-0.21422\) | \(\Gamma_0(N)\)-optimal |
306.d2 | 306d2 | \([1, -1, 1, 67, -201]\) | \(46268279/46818\) | \(-34130322\) | \([2]\) | \(128\) | \(0.13235\) |
Rank
sage: E.rank()
The elliptic curves in class 306d have rank \(0\).
Complex multiplication
The elliptic curves in class 306d do not have complex multiplication.Modular form 306.2.a.d
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.