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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 53312.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.n1 | 53312ci2 | \([0, 1, 0, -56513, 4514047]\) | \(5177717000/693889\) | \(2675027049218048\) | \([2]\) | \(344064\) | \(1.6878\) | |
53312.n2 | 53312ci1 | \([0, 1, 0, -54553, 4886055]\) | \(37259704000/833\) | \(401414623232\) | \([2]\) | \(172032\) | \(1.3412\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53312.n have rank \(0\).
Complex multiplication
The elliptic curves in class 53312.n do not have complex multiplication.Modular form 53312.2.a.n
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.