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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 53361.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.y1 | 53361bb2 | \([0, 0, 1, -18000444, -29394219605]\) | \(35084566528/1029\) | \(18917886887303448429\) | \([]\) | \(2433024\) | \(2.7987\) | |
53361.y2 | 53361bb1 | \([0, 0, 1, -391314, 28875712]\) | \(360448/189\) | \(3474713918076143589\) | \([]\) | \(811008\) | \(2.2494\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53361.y have rank \(0\).
Complex multiplication
The elliptic curves in class 53361.y do not have complex multiplication.Modular form 53361.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.