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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 102960dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.h4 | 102960dm1 | \([0, 0, 0, -12195115923, 531710999255122]\) | \(-67172890180943415009710808721/2029083623424000000000000\) | \(-6058811234206089216000000000000\) | \([2]\) | \(222953472\) | \(4.6844\) | \(\Gamma_0(N)\)-optimal |
| 102960.h3 | 102960dm2 | \([0, 0, 0, -196515115923, 33530631191255122]\) | \(281076231077501634961715630808721/245403072288481536000000\) | \(732769647404249250791424000000\) | \([2, 2]\) | \(445906944\) | \(5.0310\) | |
| 102960.h2 | 102960dm3 | \([0, 0, 0, -197909035923, 33030814133207122]\) | \(287099942490903701230558394328721/8299347173197257908489616000\) | \(24781717869612240958623457542144000\) | \([2]\) | \(891813888\) | \(5.3775\) | |
| 102960.h1 | 102960dm4 | \([0, 0, 0, -3144241195923, 2145961340537303122]\) | \(1151287518770166280399859009187288721/877598977782384000\) | \(2620496506074554105856000\) | \([2]\) | \(891813888\) | \(5.3775\) |
Rank
sage: E.rank()
The elliptic curves in class 102960dm have rank \(0\).
Complex multiplication
The elliptic curves in class 102960dm do not have complex multiplication.Modular form 102960.2.a.dm
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.
