Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 301530.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.f1 | 301530f2 | \([1, 1, 0, -210288, -37155132]\) | \(6947097508441/10687500\) | \(1582133563687500\) | \([2]\) | \(2162688\) | \(1.8158\) | |
301530.f2 | 301530f1 | \([1, 1, 0, -9268, -931328]\) | \(-594823321/2166000\) | \(-320645735574000\) | \([2]\) | \(1081344\) | \(1.4692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301530.f have rank \(0\).
Complex multiplication
The elliptic curves in class 301530.f do not have complex multiplication.Modular form 301530.2.a.f
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.