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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 6450.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6450.y1 | 6450t4 | \([1, 1, 1, -1659338, 821959031]\) | \(32337636827233520089/3023437500000\) | \(47241210937500000\) | \([2]\) | \(184320\) | \(2.2373\) | |
6450.y2 | 6450t3 | \([1, 1, 1, -611338, -175192969]\) | \(1617141066657115609/89723013444000\) | \(1401922085062500000\) | \([2]\) | \(184320\) | \(2.2373\) | |
6450.y3 | 6450t2 | \([1, 1, 1, -111338, 10807031]\) | \(9768641617435609/2396304000000\) | \(37442250000000000\) | \([2, 2]\) | \(92160\) | \(1.8907\) | |
6450.y4 | 6450t1 | \([1, 1, 1, 16662, 1079031]\) | \(32740359775271/50724864000\) | \(-792576000000000\) | \([4]\) | \(46080\) | \(1.5441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6450.y have rank \(0\).
Complex multiplication
The elliptic curves in class 6450.y do not have complex multiplication.Modular form 6450.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.