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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 254898m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254898.m1 | 254898m1 | \([1, -1, 0, -258596676, 1601006616936]\) | \(-11060825617/2744\) | \(-474448512342412917574776\) | \([]\) | \(74027520\) | \(3.5306\) | \(\Gamma_0(N)\)-optimal |
254898.m2 | 254898m2 | \([1, -1, 0, 109730934, 5666238448506]\) | \(845095823/80707214\) | \(-13954598257143134334938705406\) | \([]\) | \(222082560\) | \(4.0799\) |
Rank
sage: E.rank()
The elliptic curves in class 254898m have rank \(1\).
Complex multiplication
The elliptic curves in class 254898m do not have complex multiplication.Modular form 254898.2.a.m
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.