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SageMath
E = EllipticCurve("is1")
E.isogeny_class()
Elliptic curves in class 158400is
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.fl1 | 158400is1 | \([0, 0, 0, -21000, -1228750]\) | \(-56197120/3267\) | \(-59541075000000\) | \([]\) | \(414720\) | \(1.3994\) | \(\Gamma_0(N)\)-optimal |
158400.fl2 | 158400is2 | \([0, 0, 0, 114000, -2173750]\) | \(8990228480/5314683\) | \(-96860097675000000\) | \([]\) | \(1244160\) | \(1.9487\) |
Rank
sage: E.rank()
The elliptic curves in class 158400is have rank \(1\).
Complex multiplication
The elliptic curves in class 158400is do not have complex multiplication.Modular form 158400.2.a.is
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.