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SageMath
E = EllipticCurve("mv1")
E.isogeny_class()
Elliptic curves in class 352800.mv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.mv1 | 352800mv2 | \([0, 0, 0, -926103675, 10847696476750]\) | \(128025588102048008/7875\) | \(5403265623000000000\) | \([2]\) | \(56623104\) | \(3.5029\) | |
352800.mv2 | 352800mv4 | \([0, 0, 0, -64830675, 126250668250]\) | \(43919722445768/15380859375\) | \(10553253169921875000000000\) | \([2]\) | \(56623104\) | \(3.5029\) | |
352800.mv3 | 352800mv1 | \([0, 0, 0, -57884925, 169474070500]\) | \(250094631024064/62015625\) | \(5318839597640625000000\) | \([2, 2]\) | \(28311552\) | \(3.1564\) | \(\Gamma_0(N)\)-optimal |
352800.mv4 | 352800mv3 | \([0, 0, 0, -50994300, 211341508000]\) | \(-2671731885376/1969120125\) | \(-10808562873874248000000000\) | \([2]\) | \(56623104\) | \(3.5029\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.mv have rank \(0\).
Complex multiplication
The elliptic curves in class 352800.mv do not have complex multiplication.Modular form 352800.2.a.mv
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.