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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 30912.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30912.cc1 | 30912t2 | \([0, 1, 0, -214177, 33256895]\) | \(4144806984356137/568114785504\) | \(148927882331160576\) | \([2]\) | \(368640\) | \(2.0221\) | |
30912.cc2 | 30912t1 | \([0, 1, 0, 21343, 2780607]\) | \(4101378352343/15049939968\) | \(-3945251462971392\) | \([2]\) | \(184320\) | \(1.6755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30912.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 30912.cc do not have complex multiplication.Modular form 30912.2.a.cc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.