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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 56350q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56350.z2 | 56350q1 | \([1, 1, 0, -1164460525, -15286931899875]\) | \(276946345316184817447/168724869939200\) | \(106385267072696729600000000\) | \([2]\) | \(36556800\) | \(3.9372\) | \(\Gamma_0(N)\)-optimal |
56350.z1 | 56350q2 | \([1, 1, 0, -1383980525, -9119078459875]\) | \(464955364840944779047/212103737413882880\) | \(133736732231734782555440000000\) | \([2]\) | \(73113600\) | \(4.2838\) |
Rank
sage: E.rank()
The elliptic curves in class 56350q have rank \(1\).
Complex multiplication
The elliptic curves in class 56350q do not have complex multiplication.Modular form 56350.2.a.q
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.