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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 390390.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 390390.l1 | 390390l3 | \([1, 1, 0, -15076647173, 712527190485453]\) | \(78519570041710065450485106721/96428056919040\) | \(465439812989334543360\) | \([2]\) | \(424673280\) | \(4.1399\) | |
| 390390.l2 | 390390l6 | \([1, 1, 0, -4434325093, -104028716181203]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(905437821551647567075410117600\) | \([2]\) | \(849346560\) | \(4.4865\) | |
| 390390.l3 | 390390l4 | \([1, 1, 0, -984697093, 10076009025997]\) | \(21876183941534093095979041/3572502915711058560000\) | \(17243789226080378856935040000\) | \([2, 2]\) | \(424673280\) | \(4.1399\) | |
| 390390.l4 | 390390l2 | \([1, 1, 0, -942298373, 11132746243533]\) | \(19170300594578891358373921/671785075055001600\) | \(3242578246341157217894400\) | \([2, 2]\) | \(212336640\) | \(3.7933\) | |
| 390390.l5 | 390390l1 | \([1, 1, 0, -56251653, 190246460877]\) | \(-4078208988807294650401/880065599546327040\) | \(-4247908556480607273615360\) | \([2]\) | \(106168320\) | \(3.4468\) | \(\Gamma_0(N)\)-optimal |
| 390390.l6 | 390390l5 | \([1, 1, 0, 1786551387, 56550400285293]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-1746421304900519132172787500000\) | \([2]\) | \(849346560\) | \(4.4865\) |
Rank
sage: E.rank()
The elliptic curves in class 390390.l have rank \(0\).
Complex multiplication
The elliptic curves in class 390390.l do not have complex multiplication.Modular form 390390.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
