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SageMath
E = EllipticCurve("mn1")
E.isogeny_class()
Elliptic curves in class 310464mn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.mn3 | 310464mn1 | \([0, 0, 0, -58359, 5426260]\) | \(4004529472/99\) | \(543414142656\) | \([2]\) | \(786432\) | \(1.3609\) | \(\Gamma_0(N)\)-optimal |
| 310464.mn2 | 310464mn2 | \([0, 0, 0, -60564, 4994080]\) | \(69934528/9801\) | \(3443072007868416\) | \([2, 2]\) | \(1572864\) | \(1.7075\) | |
| 310464.mn4 | 310464mn3 | \([0, 0, 0, 98196, 26775952]\) | \(37259704/131769\) | \(-370321522624069632\) | \([2]\) | \(3145728\) | \(2.0541\) | |
| 310464.mn1 | 310464mn4 | \([0, 0, 0, -254604, -44447312]\) | \(649461896/72171\) | \(202828241918066688\) | \([2]\) | \(3145728\) | \(2.0541\) |
Rank
sage: E.rank()
The elliptic curves in class 310464mn have rank \(1\).
Complex multiplication
The elliptic curves in class 310464mn do not have complex multiplication.Modular form 310464.2.a.mn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
