Show commands:
SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 93600.dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.dp1 | 93600eb2 | \([0, 0, 0, -7473675, -7863776750]\) | \(7916055336451592/385003125\) | \(2245338225000000000\) | \([2]\) | \(2211840\) | \(2.5937\) | |
93600.dp2 | 93600eb1 | \([0, 0, 0, -442425, -136433000]\) | \(-13137573612736/3427734375\) | \(-2498818359375000000\) | \([2]\) | \(1105920\) | \(2.2472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93600.dp have rank \(0\).
Complex multiplication
The elliptic curves in class 93600.dp do not have complex multiplication.Modular form 93600.2.a.dp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.