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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 304200l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.l2 | 304200l1 | \([0, 0, 0, -570375, -370743750]\) | \(-432\) | \(-47503040773500000000\) | \([2]\) | \(8294400\) | \(2.4640\) | \(\Gamma_0(N)\)-optimal |
| 304200.l1 | 304200l2 | \([0, 0, 0, -11977875, -15941981250]\) | \(1000188\) | \(190012163094000000000\) | \([2]\) | \(16588800\) | \(2.8106\) |
Rank
sage: E.rank()
The elliptic curves in class 304200l have rank \(0\).
Complex multiplication
The elliptic curves in class 304200l do not have complex multiplication.Modular form 304200.2.a.l
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.
