Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 122010.dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122010.dj1 | 122010do1 | \([1, 0, 0, -312566640, -2126999407968]\) | \(-68921624431417353829938395089/117227740275188640\) | \(-5744159273484243360\) | \([]\) | \(20885760\) | \(3.2892\) | \(\Gamma_0(N)\)-optimal |
122010.dj2 | 122010do2 | \([1, 0, 0, 975016510, -11270628771900]\) | \(2092008964199791878427102647311/2330581636033743421440000000\) | \(-114198500165653427650560000000\) | \([7]\) | \(146200320\) | \(4.2621\) |
Rank
sage: E.rank()
The elliptic curves in class 122010.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 122010.dj do not have complex multiplication.Modular form 122010.2.a.dj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.