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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 391460.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 391460.m1 | 391460m2 | \([0, 1, 0, -6359285, 6170368775]\) | \(750484394082304/578125\) | \(21909311572000000\) | \([]\) | \(5474304\) | \(2.4433\) | |
| 391460.m2 | 391460m1 | \([0, 1, 0, -95925, 4404023]\) | \(2575826944/1266325\) | \(47990156067308800\) | \([]\) | \(1824768\) | \(1.8940\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 391460.m have rank \(0\).
Complex multiplication
The elliptic curves in class 391460.m do not have complex multiplication.Modular form 391460.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
