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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 25200.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.ft1 | 25200es2 | \([0, 0, 0, -1261875, -577268750]\) | \(-7620530425/526848\) | \(-15362887680000000000\) | \([]\) | \(622080\) | \(2.4325\) | |
25200.ft2 | 25200es1 | \([0, 0, 0, 88125, -818750]\) | \(2595575/1512\) | \(-44089920000000000\) | \([]\) | \(207360\) | \(1.8832\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.ft have rank \(0\).
Complex multiplication
The elliptic curves in class 25200.ft do not have complex multiplication.Modular form 25200.2.a.ft
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.