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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 118580h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118580.i2 | 118580h1 | \([0, -1, 0, -31621, -10608079]\) | \(-65536/875\) | \(-46686613139936000\) | \([]\) | \(777600\) | \(1.8801\) | \(\Gamma_0(N)\)-optimal |
118580.i1 | 118580h2 | \([0, -1, 0, -4774821, -4014343199]\) | \(-225637236736/1715\) | \(-91505761754274560\) | \([]\) | \(2332800\) | \(2.4295\) |
Rank
sage: E.rank()
The elliptic curves in class 118580h have rank \(0\).
Complex multiplication
The elliptic curves in class 118580h do not have complex multiplication.Modular form 118580.2.a.h
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.