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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 471600.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
471600.m1 | 471600m1 | \([0, 0, 0, -255675, -49513750]\) | \(39616946929/226368\) | \(10561425408000000\) | \([2]\) | \(4423680\) | \(1.9161\) | \(\Gamma_0(N)\)-optimal |
471600.m2 | 471600m2 | \([0, 0, 0, -111675, -104953750]\) | \(-3301293169/100082952\) | \(-4669470208512000000\) | \([2]\) | \(8847360\) | \(2.2627\) |
Rank
sage: E.rank()
The elliptic curves in class 471600.m have rank \(1\).
Complex multiplication
The elliptic curves in class 471600.m do not have complex multiplication.Modular form 471600.2.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.