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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1452e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1452.h2 | 1452e1 | \([0, 1, 0, -524, -5436]\) | \(-4253392/729\) | \(-2732361984\) | \([3]\) | \(1008\) | \(0.53707\) | \(\Gamma_0(N)\)-optimal |
1452.h1 | 1452e2 | \([0, 1, 0, -44084, -3577356]\) | \(-2527934627152/9\) | \(-33732864\) | \([]\) | \(3024\) | \(1.0864\) |
Rank
sage: E.rank()
The elliptic curves in class 1452e have rank \(0\).
Complex multiplication
The elliptic curves in class 1452e do not have complex multiplication.Modular form 1452.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.