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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 56448.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56448.cc1 | 56448q2 | \([0, 0, 0, -5880, -142688]\) | \(16000/3\) | \(4215576379392\) | \([2]\) | \(92160\) | \(1.1404\) | |
56448.cc2 | 56448q1 | \([0, 0, 0, 735, -13034]\) | \(4000/9\) | \(-98802571392\) | \([2]\) | \(46080\) | \(0.79382\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56448.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 56448.cc do not have complex multiplication.Modular form 56448.2.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.