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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 474320.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474320.cl1 | 474320cl1 | \([0, -1, 0, -120556, 16161356]\) | \(-177953104/125\) | \(-136112574752000\) | \([]\) | \(1866240\) | \(1.6483\) | \(\Gamma_0(N)\)-optimal |
474320.cl2 | 474320cl2 | \([0, -1, 0, 116604, 68431420]\) | \(161017136/1953125\) | \(-2126758980500000000\) | \([]\) | \(5598720\) | \(2.1976\) |
Rank
sage: E.rank()
The elliptic curves in class 474320.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 474320.cl do not have complex multiplication.Modular form 474320.2.a.cl
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.