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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 338130m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.m2 | 338130m1 | \([1, -1, 0, 10350, 1122336]\) | \(6967871/35100\) | \(-617629701815100\) | \([2]\) | \(1597440\) | \(1.5203\) | \(\Gamma_0(N)\)-optimal |
338130.m1 | 338130m2 | \([1, -1, 0, -119700, 14309406]\) | \(10779215329/1232010\) | \(21678802533710010\) | \([2]\) | \(3194880\) | \(1.8669\) |
Rank
sage: E.rank()
The elliptic curves in class 338130m have rank \(0\).
Complex multiplication
The elliptic curves in class 338130m do not have complex multiplication.Modular form 338130.2.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.