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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 224400.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.fm1 | 224400bo2 | \([0, 1, 0, -72808, -7585612]\) | \(666940371553/37026\) | \(2369664000000\) | \([2]\) | \(589824\) | \(1.4399\) | |
224400.fm2 | 224400bo1 | \([0, 1, 0, -4808, -105612]\) | \(192100033/38148\) | \(2441472000000\) | \([2]\) | \(294912\) | \(1.0933\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.fm have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.fm do not have complex multiplication.Modular form 224400.2.a.fm
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.