Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 14450l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14450.d3 | 14450l1 | \([1, 1, 0, -150, -8450]\) | \(-25/2\) | \(-30171961250\) | \([]\) | \(10080\) | \(0.69051\) | \(\Gamma_0(N)\)-optimal |
14450.d1 | 14450l2 | \([1, 1, 0, -36275, -2674475]\) | \(-349938025/8\) | \(-120687845000\) | \([]\) | \(30240\) | \(1.2398\) | |
14450.d2 | 14450l3 | \([1, 1, 0, -21825, 1487125]\) | \(-121945/32\) | \(-301719612500000\) | \([]\) | \(50400\) | \(1.4952\) | |
14450.d4 | 14450l4 | \([1, 1, 0, 158800, -10976000]\) | \(46969655/32768\) | \(-308960883200000000\) | \([]\) | \(151200\) | \(2.0445\) |
Rank
sage: E.rank()
The elliptic curves in class 14450l have rank \(0\).
Complex multiplication
The elliptic curves in class 14450l do not have complex multiplication.Modular form 14450.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.