Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 135252e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135252.g1 | 135252e1 | \([0, 0, 0, -3249516, -2254590439]\) | \(13478411517952/304317\) | \(85677592235790672\) | \([2]\) | \(2211840\) | \(2.3632\) | \(\Gamma_0(N)\)-optimal |
| 135252.g2 | 135252e2 | \([0, 0, 0, -3132471, -2424516370]\) | \(-754612278352/127035441\) | \(-572250158275316541696\) | \([2]\) | \(4423680\) | \(2.7098\) |
Rank
sage: E.rank()
The elliptic curves in class 135252e have rank \(1\).
Complex multiplication
The elliptic curves in class 135252e do not have complex multiplication.Modular form 135252.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
