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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 35574.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.m1 | 35574m2 | \([1, 1, 0, -311029534, 2111144052340]\) | \(46546832455691959/748268928\) | \(53492904885698769085056\) | \([2]\) | \(9031680\) | \(3.4940\) | |
| 35574.m2 | 35574m1 | \([1, 1, 0, -18848414, 35080322292]\) | \(-10358806345399/1445216256\) | \(-103316886253859899686912\) | \([2]\) | \(4515840\) | \(3.1475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35574.m have rank \(1\).
Complex multiplication
The elliptic curves in class 35574.m do not have complex multiplication.Modular form 35574.2.a.m
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.
