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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 14450c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.n2 | 14450c1 | \([1, 0, 1, 2882624, -584559602]\) | \(7023836099951/4456448000\) | \(-1680747204608000000000\) | \([]\) | \(580608\) | \(2.7618\) | \(\Gamma_0(N)\)-optimal |
14450.n1 | 14450c2 | \([1, 0, 1, -47981376, -132054127602]\) | \(-32391289681150609/1228250000000\) | \(-463233892566406250000000\) | \([]\) | \(1741824\) | \(3.3111\) |
Rank
sage: E.rank()
The elliptic curves in class 14450c have rank \(1\).
Complex multiplication
The elliptic curves in class 14450c do not have complex multiplication.Modular form 14450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.