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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 103488fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103488.b2 | 103488fu1 | \([0, -1, 0, -658625, -245247519]\) | \(-4097989445764/1004475087\) | \(-7744748880557703168\) | \([2]\) | \(2949120\) | \(2.3427\) | \(\Gamma_0(N)\)-optimal |
103488.b1 | 103488fu2 | \([0, -1, 0, -11093665, -14217766079]\) | \(9791533777258802/427901859\) | \(6598456221301604352\) | \([2]\) | \(5898240\) | \(2.6893\) |
Rank
sage: E.rank()
The elliptic curves in class 103488fu have rank \(1\).
Complex multiplication
The elliptic curves in class 103488fu do not have complex multiplication.Modular form 103488.2.a.fu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.