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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 46784f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46784.o2 | 46784f1 | \([0, 0, 0, -3692, -84560]\) | \(21230922609/502928\) | \(131839557632\) | \([2]\) | \(55296\) | \(0.91894\) | \(\Gamma_0(N)\)-optimal |
46784.o1 | 46784f2 | \([0, 0, 0, -58732, -5478480]\) | \(85468909049649/49708\) | \(13030653952\) | \([2]\) | \(110592\) | \(1.2655\) |
Rank
sage: E.rank()
The elliptic curves in class 46784f have rank \(0\).
Complex multiplication
The elliptic curves in class 46784f do not have complex multiplication.Modular form 46784.2.a.f
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.