Show commands:
SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 203280cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.dm1 | 203280cn1 | \([0, -1, 0, -271685, 112857417]\) | \(-4890195460096/9282994875\) | \(-4210020271039968000\) | \([]\) | \(3732480\) | \(2.2635\) | \(\Gamma_0(N)\)-optimal |
203280.dm2 | 203280cn2 | \([0, -1, 0, 2341915, -2390187303]\) | \(3132137615458304/7250937873795\) | \(-3288442560163364862720\) | \([]\) | \(11197440\) | \(2.8128\) |
Rank
sage: E.rank()
The elliptic curves in class 203280cn have rank \(1\).
Complex multiplication
The elliptic curves in class 203280cn do not have complex multiplication.Modular form 203280.2.a.cn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.