Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 126350.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.s1 | 126350bv2 | \([1, 1, 0, -269409975, 983940363925]\) | \(73546685675688065425/28334561366578432\) | \(833140251399528930649120000\) | \([]\) | \(78382080\) | \(3.8646\) | |
126350.s2 | 126350bv1 | \([1, 1, 0, -119233975, -501122375275]\) | \(6375616158287489425/805524471808\) | \(23685380277041889280000\) | \([]\) | \(26127360\) | \(3.3153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126350.s have rank \(0\).
Complex multiplication
The elliptic curves in class 126350.s do not have complex multiplication.Modular form 126350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.