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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 76050m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.k2 | 76050m1 | \([1, -1, 0, -7032, 228736]\) | \(337135557915/64\) | \(7300800\) | \([]\) | \(82944\) | \(0.70923\) | \(\Gamma_0(N)\)-optimal |
76050.k1 | 76050m2 | \([1, -1, 0, -8007, 161981]\) | \(682724835/262144\) | \(21800071987200\) | \([]\) | \(248832\) | \(1.2585\) |
Rank
sage: E.rank()
The elliptic curves in class 76050m have rank \(1\).
Complex multiplication
The elliptic curves in class 76050m do not have complex multiplication.Modular form 76050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.