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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 4900.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.m1 | 4900p1 | \([0, 0, 0, -98000, 11790625]\) | \(28311552/49\) | \(180150031250000\) | \([2]\) | \(17280\) | \(1.6293\) | \(\Gamma_0(N)\)-optimal |
4900.m2 | 4900p2 | \([0, 0, 0, -67375, 19293750]\) | \(-574992/2401\) | \(-141237624500000000\) | \([2]\) | \(34560\) | \(1.9759\) |
Rank
sage: E.rank()
The elliptic curves in class 4900.m have rank \(0\).
Complex multiplication
The elliptic curves in class 4900.m do not have complex multiplication.Modular form 4900.2.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 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.