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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 73920di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.hi3 | 73920di1 | \([0, 1, 0, -705, -5985]\) | \(148035889/31185\) | \(8174960640\) | \([2]\) | \(49152\) | \(0.61672\) | \(\Gamma_0(N)\)-optimal |
| 73920.hi2 | 73920di2 | \([0, 1, 0, -3585, 76383]\) | \(19443408769/1334025\) | \(349706649600\) | \([2, 2]\) | \(98304\) | \(0.96329\) | |
| 73920.hi4 | 73920di3 | \([0, 1, 0, 3135, 335775]\) | \(12994449551/192163125\) | \(-50374410240000\) | \([2]\) | \(196608\) | \(1.3099\) | |
| 73920.hi1 | 73920di4 | \([0, 1, 0, -56385, 5134623]\) | \(75627935783569/396165\) | \(103852277760\) | \([2]\) | \(196608\) | \(1.3099\) |
Rank
sage: E.rank()
The elliptic curves in class 73920di have rank \(0\).
Complex multiplication
The elliptic curves in class 73920di do not have complex multiplication.Modular form 73920.2.a.di
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.
