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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 7245m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7245.p1 | 7245m1 | \([1, -1, 0, -1464, 21923]\) | \(476196576129/197225\) | \(143777025\) | \([2]\) | \(4608\) | \(0.52729\) | \(\Gamma_0(N)\)-optimal |
7245.p2 | 7245m2 | \([1, -1, 0, -1239, 28718]\) | \(-288673724529/311181605\) | \(-226851390045\) | \([2]\) | \(9216\) | \(0.87386\) |
Rank
sage: E.rank()
The elliptic curves in class 7245m have rank \(1\).
Complex multiplication
The elliptic curves in class 7245m do not have complex multiplication.Modular form 7245.2.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.