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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 207214c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207214.r2 | 207214c1 | \([1, 0, 0, -744209, -247149911]\) | \(968917714969177/100803584\) | \(4742393417237504\) | \([2]\) | \(3421440\) | \(2.0401\) | \(\Gamma_0(N)\)-optimal |
207214.r1 | 207214c2 | \([1, 0, 0, -801969, -206567735]\) | \(1212480836738137/310100175392\) | \(14588935949571160352\) | \([2]\) | \(6842880\) | \(2.3867\) |
Rank
sage: E.rank()
The elliptic curves in class 207214c have rank \(0\).
Complex multiplication
The elliptic curves in class 207214c do not have complex multiplication.Modular form 207214.2.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 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.