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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 7360w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7360.v1 | 7360w1 | \([0, 1, 0, -185, -4417]\) | \(-687518464/7604375\) | \(-7786880000\) | \([]\) | \(4608\) | \(0.57999\) | \(\Gamma_0(N)\)-optimal |
7360.v2 | 7360w2 | \([0, 1, 0, 1655, 112975]\) | \(489277573376/5615234375\) | \(-5750000000000\) | \([]\) | \(13824\) | \(1.1293\) |
Rank
sage: E.rank()
The elliptic curves in class 7360w have rank \(1\).
Complex multiplication
The elliptic curves in class 7360w do not have complex multiplication.Modular form 7360.2.a.w
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.