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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 302549.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302549.c1 | 302549c2 | \([1, -1, 0, -16041514, 24733556859]\) | \(177930109857804849/634933\) | \(1629064366045597\) | \([2]\) | \(11923200\) | \(2.5606\) | |
302549.c2 | 302549c1 | \([1, -1, 0, -1003049, 386282024]\) | \(43499078731809/82055753\) | \(210532612482480977\) | \([2]\) | \(5961600\) | \(2.2141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302549.c have rank \(0\).
Complex multiplication
The elliptic curves in class 302549.c do not have complex multiplication.Modular form 302549.2.a.c
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.