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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 381150ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.ev3 | 381150ev1 | \([1, -1, 0, -1525167, 14108653741]\) | \(-19443408769/4249907200\) | \(-85759672187851200000000\) | \([2]\) | \(39813120\) | \(3.0798\) | \(\Gamma_0(N)\)-optimal |
| 381150.ev2 | 381150ev2 | \([1, -1, 0, -97357167, 366482917741]\) | \(5057359576472449/51765560000\) | \(1044586916208556875000000\) | \([2]\) | \(79626240\) | \(3.4263\) | |
| 381150.ev4 | 381150ev3 | \([1, -1, 0, 13720833, -380046184259]\) | \(14156681599871/3100231750000\) | \(-62560156275028371093750000\) | \([2]\) | \(119439360\) | \(3.6291\) | |
| 381150.ev1 | 381150ev4 | \([1, -1, 0, -711008667, -7090316624759]\) | \(1969902499564819009/63690429687500\) | \(1285221091769577026367187500\) | \([2]\) | \(238878720\) | \(3.9756\) |
Rank
sage: E.rank()
The elliptic curves in class 381150ev have rank \(2\).
Complex multiplication
The elliptic curves in class 381150ev do not have complex multiplication.Modular form 381150.2.a.ev
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
