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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 20510e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20510.c2 | 20510e1 | \([1, -1, 1, 9588, 2333199]\) | \(97487796040631919/2412980990000000\) | \(-2412980990000000\) | \([7]\) | \(395136\) | \(1.6318\) | \(\Gamma_0(N)\)-optimal |
20510.c1 | 20510e2 | \([1, -1, 1, -5545962, -5028652761]\) | \(-18864891308791949569351281/12976912684820654990\) | \(-12976912684820654990\) | \([]\) | \(2765952\) | \(2.6048\) |
Rank
sage: E.rank()
The elliptic curves in class 20510e have rank \(0\).
Complex multiplication
The elliptic curves in class 20510e do not have complex multiplication.Modular form 20510.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.