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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 24400a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24400.s2 | 24400a1 | \([0, 0, 0, -550, 4875]\) | \(73598976/1525\) | \(381250000\) | \([2]\) | \(9216\) | \(0.43676\) | \(\Gamma_0(N)\)-optimal |
24400.s1 | 24400a2 | \([0, 0, 0, -1175, -8250]\) | \(44851536/18605\) | \(74420000000\) | \([2]\) | \(18432\) | \(0.78333\) |
Rank
sage: E.rank()
The elliptic curves in class 24400a have rank \(1\).
Complex multiplication
The elliptic curves in class 24400a do not have complex multiplication.Modular form 24400.2.a.a
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.