Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 152460.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.i1 | 152460bc2 | \([0, 0, 0, -4552383, 3459963782]\) | \(31558509702736/2620631475\) | \(866422171780025414400\) | \([2]\) | \(6635520\) | \(2.7597\) | |
| 152460.i2 | 152460bc1 | \([0, 0, 0, 299112, 247303793]\) | \(143225913344/1361505915\) | \(-28133460461224586160\) | \([2]\) | \(3317760\) | \(2.4131\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.i have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.i do not have complex multiplication.Modular form 152460.2.a.i
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.
