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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 224400.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.fl1 | 224400bt1 | \([0, 1, 0, -78408, 8419188]\) | \(832972004929/610368\) | \(39063552000000\) | \([2]\) | \(737280\) | \(1.5422\) | \(\Gamma_0(N)\)-optimal |
224400.fl2 | 224400bt2 | \([0, 1, 0, -62408, 11971188]\) | \(-420021471169/727634952\) | \(-46568636928000000\) | \([2]\) | \(1474560\) | \(1.8888\) |
Rank
sage: E.rank()
The elliptic curves in class 224400.fl have rank \(2\).
Complex multiplication
The elliptic curves in class 224400.fl do not have complex multiplication.Modular form 224400.2.a.fl
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.