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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 250470m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.m2 | 250470m1 | \([1, -1, 0, 69855, -13294979]\) | \(788120875053/2048288000\) | \(-97974012714336000\) | \([2]\) | \(2580480\) | \(1.9440\) | \(\Gamma_0(N)\)-optimal |
250470.m1 | 250470m2 | \([1, -1, 0, -598065, -149417075]\) | \(494594642264787/84185750000\) | \(4026785169305250000\) | \([2]\) | \(5160960\) | \(2.2906\) |
Rank
sage: E.rank()
The elliptic curves in class 250470m have rank \(1\).
Complex multiplication
The elliptic curves in class 250470m do not have complex multiplication.Modular form 250470.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.