Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 56350t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56350.i2 | 56350t1 | \([1, 0, 1, -23764501, 44564919648]\) | \(276946345316184817447/168724869939200\) | \(904259849830400000000\) | \([2]\) | \(5222400\) | \(2.9642\) | \(\Gamma_0(N)\)-optimal |
56350.i1 | 56350t2 | \([1, 0, 1, -28244501, 26582199648]\) | \(464955364840944779047/212103737413882880\) | \(1136743467702528560000000\) | \([2]\) | \(10444800\) | \(3.3108\) |
Rank
sage: E.rank()
The elliptic curves in class 56350t have rank \(1\).
Complex multiplication
The elliptic curves in class 56350t do not have complex multiplication.Modular form 56350.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.