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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 270802.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270802.s1 | 270802s2 | \([1, -1, 1, -532766089, -4733046276727]\) | \(28115476317271727409033/150871003136\) | \(89741591127956934656\) | \([2]\) | \(46448640\) | \(3.4442\) | |
| 270802.s2 | 270802s1 | \([1, -1, 1, -33279369, -74033947255]\) | \(-6852688047169144713/15901562765312\) | \(-9458620373152827441152\) | \([2]\) | \(23224320\) | \(3.0976\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270802.s have rank \(0\).
Complex multiplication
The elliptic curves in class 270802.s do not have complex multiplication.Modular form 270802.2.a.s
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 LMFDB 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 LMFDB labels.
